<?xml version="1.0" encoding="us-ascii"?>
<!-- XBRL document created with Praxa -->
<!-- Copyright (c) 2026 Praxa LLC. All Rights Reserved.-->
<!-- Creation Date: 2026-10-28T18:27:38.8344+00:00 -->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/all" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#all" xlink:type="simple" />
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-default" xlink:type="simple" />
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-domain" xlink:type="simple" />
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/domain-member" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#domain-member" xlink:type="simple" />
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#hypercube-dimension" xlink:type="simple" />
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/notAll" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#notAll" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/NatureofBusinessandOrganizationDetails" xlink:href="glxg-20260630.xsd#NatureofBusinessandOrganizationDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/SummaryofSignificantAccountingPoliciesDetails" xlink:href="glxg-20260630.xsd#SummaryofSignificantAccountingPoliciesDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/NatureofBusinessandOrganizationScheduleofConsolidatedFinancialStatementsDetails" xlink:href="glxg-20260630.xsd#NatureofBusinessandOrganizationScheduleofConsolidatedFinancialStatementsDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/RevenuesScheduleofRevenuesDisaggregatedbyServiceLinesandGeographicLocationDetails" xlink:href="glxg-20260630.xsd#RevenuesScheduleofRevenuesDisaggregatedbyServiceLinesandGeographicLocationDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/TaxesDetails" xlink:href="glxg-20260630.xsd#TaxesDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/TaxesScheduleofIncomeTaxProvisionDetails" xlink:href="glxg-20260630.xsd#TaxesScheduleofIncomeTaxProvisionDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/PropertyandEquipmentNetScheduleofPropertyandEquipmentDetails" xlink:href="glxg-20260630.xsd#PropertyandEquipmentNetScheduleofPropertyandEquipmentDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/ConsolidatedBalanceSheetsParentheticals" xlink:href="glxg-20260630.xsd#ConsolidatedBalanceSheetsParentheticals" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/ConsolidatedStatementsofIncomeLossandComprehensiveIncomeLossParentheticals" xlink:href="glxg-20260630.xsd#ConsolidatedStatementsofIncomeLossandComprehensiveIncomeLossParentheticals" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/ShareBasedCompensationDetails" xlink:href="glxg-20260630.xsd#ShareBasedCompensationDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/ConsolidatedStatementsofIncomeLossandComprehensiveIncomeLoss" xlink:href="glxg-20260630.xsd#ConsolidatedStatementsofIncomeLossandComprehensiveIncomeLoss" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/SubsequentEventsDetails" xlink:href="glxg-20260630.xsd#SubsequentEventsDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/EquityDetails" xlink:href="glxg-20260630.xsd#EquityDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/DocumentAndEntityInformation" xlink:href="glxg-20260630.xsd#DocumentAndEntityInformation" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/ConsolidatedStatementsofChangesinShareholdersEquity" xlink:href="glxg-20260630.xsd#ConsolidatedStatementsofChangesinShareholdersEquity" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/SummaryofSignificantAccountingPoliciesScheduleofEstimatedUsefulLivesDetails" xlink:href="glxg-20260630.xsd#SummaryofSignificantAccountingPoliciesScheduleofEstimatedUsefulLivesDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/RevenuesScheduleofGroupsRevenuesDisaggregatedbyServiceLinesDetails" xlink:href="glxg-20260630.xsd#RevenuesScheduleofGroupsRevenuesDisaggregatedbyServiceLinesDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/ConsolidatedBalanceSheets" xlink:href="glxg-20260630.xsd#ConsolidatedBalanceSheets" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/RelatedPartyTransactionsScheduleofTransactionswithRelatedPartiesDetails" xlink:href="glxg-20260630.xsd#RelatedPartyTransactionsScheduleofTransactionswithRelatedPartiesDetails" xlink:type="simple" />
  <link:roleRef roleURI="http://galaxy-hk.com/20260630/role/ConsolidatedStatementsofChangesinShareholdersEquityParentheticals" xlink:href="glxg-20260630.xsd#ConsolidatedStatementsofChangesinShareholdersEquityParentheticals" xlink:type="simple" />
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/NatureofBusinessandOrganizationDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_MelkwegCaymanMember" xlink:label="glxg_MelkwegCaymanMember_1470" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_NatureofBusinessandOrganizationDetailsTable" xlink:label="glxg_NatureofBusinessandOrganizationDetailsTable_1468" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipAxis" xlink:label="srt_OwnershipAxis_1469" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipDomain" xlink:label="srt_OwnershipDomain_1716" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_1472" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_1467" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:label="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_1471" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipDomain" xlink:label="srt_OwnershipDomain_1716_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_OwnershipDomain_1716" xlink:to="glxg_MelkwegCaymanMember_1470" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_1471" xlink:to="glxg_NatureofBusinessandOrganizationDetailsTable_1468" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_NatureofBusinessandOrganizationDetailsTable_1468" xlink:to="srt_OwnershipAxis_1469" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_OwnershipAxis_1469" xlink:to="srt_OwnershipDomain_1716" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_1471" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByParent_1472" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_OwnershipAxis_1469" xlink:to="srt_OwnershipDomain_1716_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/SummaryofSignificantAccountingPoliciesDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_OneVendorMember" xlink:label="glxg_OneVendorMember_1486" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_EmploymentServicesMember" xlink:label="glxg_EmploymentServicesMember_1796" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PayrollOutsourcingServicesMember" xlink:label="glxg_PayrollOutsourcingServicesMember_1797" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_CustomerOneMember" xlink:label="glxg_CustomerOneMember_1499" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_CustomerTwoMember" xlink:label="glxg_CustomerTwoMember_1500" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_CustomerThreeMember" xlink:label="glxg_CustomerThreeMember_1501" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_CustomerFourMember" xlink:label="glxg_CustomerFourMember_1502" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_HongKongMandatoryProvidentFundSchemesMember" xlink:label="glxg_HongKongMandatoryProvidentFundSchemesMember_1491" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_VendorMember" xlink:label="glxg_VendorMember_1485" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TwoVendorMember" xlink:label="glxg_TwoVendorMember_1487" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ThreeVendorMember" xlink:label="glxg_ThreeVendorMember_1488" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableMember" xlink:label="us-gaap_AccountsReceivableMember_1511" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SalesRevenueNetMember" xlink:label="us-gaap_SalesRevenueNetMember_1512" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableMember" xlink:label="us-gaap_AccountsPayableMember_1513" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerConcentrationRiskMember" xlink:label="us-gaap_CustomerConcentrationRiskMember_1494" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplierConcentrationRiskMember" xlink:label="us-gaap_SupplierConcentrationRiskMember_1495" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditConcentrationRiskMember" xlink:label="us-gaap_CreditConcentrationRiskMember_1496" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember" xlink:label="srt_RangeMember_1480" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember" xlink:label="srt_MinimumMember_1481" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember" xlink:label="srt_MaximumMember_1482" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_HKD" xlink:label="currency_HKD_1508" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PercentageOfEmployerMandatoryContributions" xlink:label="glxg_PercentageOfEmployerMandatoryContributions_1524" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_SummaryofSignificantAccountingPoliciesDetailsTable" xlink:label="glxg_SummaryofSignificantAccountingPoliciesDetailsTable_1475" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_CreditTerm" xlink:label="glxg_CreditTerm_1793" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ConsecutiveDays" xlink:label="glxg_ConsecutiveDays_1798" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_AssessableProfit" xlink:label="glxg_AssessableProfit_1802" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PercentageOfTaxBenefit" xlink:label="glxg_PercentageOfTaxBenefit_1528" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_AllCurrenciesDomain" xlink:label="currency_AllCurrenciesDomain_1506" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_USD" xlink:label="currency_USD_1507" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain" xlink:label="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain_1484" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionAxis" xlink:label="us-gaap_RelatedPartyTransactionAxis_1489" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MajorCustomersAxis" xlink:label="srt_MajorCustomersAxis_1497" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_1509" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskBenchmarkDomain" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_1510" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:label="us-gaap_LessorDirectFinancingLeaseTermOfContract1_1523" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDomain" xlink:label="us-gaap_RelatedPartyTransactionDomain_1490" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract_1474" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis" xlink:label="srt_ProductOrServiceAxis_1794" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain" xlink:label="srt_ProductsAndServicesDomain_1795" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseImpairmentLoss" xlink:label="us-gaap_OperatingLeaseImpairmentLoss_1799" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_1800" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf_1801" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_NameOfMajorCustomerDomain" xlink:label="srt_NameOfMajorCustomerDomain_1498" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskLineItems" xlink:label="us-gaap_ConcentrationRiskLineItems_1514" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:label="us-gaap_ForeignCurrencyExchangeRateTranslation1_1515" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Deposits" xlink:label="us-gaap_Deposits_1516" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Cash" xlink:label="us-gaap_Cash_1517" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvisionForDoubtfulAccounts" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_1519" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_1520" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherIncome" xlink:label="us-gaap_OtherIncome_1525" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedEmployeeBenefitsCurrent" xlink:label="us-gaap_AccruedEmployeeBenefitsCurrent_1526" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseExpense" xlink:label="us-gaap_OperatingLeaseExpense_1527" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskPercentage1" xlink:label="us-gaap_ConcentrationRiskPercentage1_1529" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionBySupplierAxis" xlink:label="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionBySupplierAxis_1483" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByTypeAxis" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_1492" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTypeDomain" xlink:label="us-gaap_ConcentrationRiskTypeDomain_1493" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CurrencyAxis" xlink:label="srt_CurrencyAxis_1505" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis_1479" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecognizedTaxBenefits" xlink:label="us-gaap_UnrecognizedTaxBenefits_34700" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingOtherItemAmount" xlink:label="us-gaap_SegmentReportingOtherItemAmount_34701" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember" xlink:label="srt_RangeMember_1480_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_AllCurrenciesDomain" xlink:label="currency_AllCurrenciesDomain_1506_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain" xlink:label="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain_1484_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskBenchmarkDomain" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_1510_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDomain" xlink:label="us-gaap_RelatedPartyTransactionDomain_1490_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain" xlink:label="srt_ProductsAndServicesDomain_1795_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_NameOfMajorCustomerDomain" xlink:label="srt_NameOfMajorCustomerDomain_1498_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTypeDomain" xlink:label="us-gaap_ConcentrationRiskTypeDomain_1493_default" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain_1484" xlink:to="glxg_OneVendorMember_1486" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ProductsAndServicesDomain_1795" xlink:to="glxg_EmploymentServicesMember_1796" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ProductsAndServicesDomain_1795" xlink:to="glxg_PayrollOutsourcingServicesMember_1797" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_NameOfMajorCustomerDomain_1498" xlink:to="glxg_CustomerOneMember_1499" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_NameOfMajorCustomerDomain_1498" xlink:to="glxg_CustomerTwoMember_1500" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_NameOfMajorCustomerDomain_1498" xlink:to="glxg_CustomerThreeMember_1501" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_NameOfMajorCustomerDomain_1498" xlink:to="glxg_CustomerFourMember_1502" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionDomain_1490" xlink:to="glxg_HongKongMandatoryProvidentFundSchemesMember_1491" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain_1484" xlink:to="glxg_VendorMember_1485" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain_1484" xlink:to="glxg_TwoVendorMember_1487" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain_1484" xlink:to="glxg_ThreeVendorMember_1488" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskBenchmarkDomain_1510" xlink:to="us-gaap_AccountsReceivableMember_1511" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskBenchmarkDomain_1510" xlink:to="us-gaap_SalesRevenueNetMember_1512" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskBenchmarkDomain_1510" xlink:to="us-gaap_AccountsPayableMember_1513" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskTypeDomain_1493" xlink:to="us-gaap_CustomerConcentrationRiskMember_1494" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskTypeDomain_1493" xlink:to="us-gaap_SupplierConcentrationRiskMember_1495" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskTypeDomain_1493" xlink:to="us-gaap_CreditConcentrationRiskMember_1496" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_RangeAxis_1479" xlink:to="srt_RangeMember_1480" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_RangeMember_1480" xlink:to="srt_MinimumMember_1481" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_RangeMember_1480" xlink:to="srt_MaximumMember_1482" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="currency_AllCurrenciesDomain_1506" xlink:to="currency_HKD_1508" />
    <link:definitionArc xlink:type="arc" order="19.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="glxg_PercentageOfEmployerMandatoryContributions_1524" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="glxg_SummaryofSignificantAccountingPoliciesDetailsTable_1475" />
    <link:definitionArc xlink:type="arc" order="96.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="glxg_CreditTerm_1793" />
    <link:definitionArc xlink:type="arc" order="99.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="glxg_ConsecutiveDays_1798" />
    <link:definitionArc xlink:type="arc" order="103.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="glxg_AssessableProfit_1802" />
    <link:definitionArc xlink:type="arc" order="23.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="glxg_PercentageOfTaxBenefit_1528" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_CurrencyAxis_1505" xlink:to="currency_AllCurrenciesDomain_1506" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="currency_AllCurrenciesDomain_1506" xlink:to="currency_USD_1507" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionBySupplierAxis_1483" xlink:to="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain_1484" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SummaryofSignificantAccountingPoliciesDetailsTable_1475" xlink:to="us-gaap_RelatedPartyTransactionAxis_1489" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SummaryofSignificantAccountingPoliciesDetailsTable_1475" xlink:to="srt_MajorCustomersAxis_1497" />
    <link:definitionArc xlink:type="arc" order="18.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SummaryofSignificantAccountingPoliciesDetailsTable_1475" xlink:to="us-gaap_ConcentrationRiskByBenchmarkAxis_1509" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_ConcentrationRiskByBenchmarkAxis_1509" xlink:to="us-gaap_ConcentrationRiskBenchmarkDomain_1510" />
    <link:definitionArc xlink:type="arc" order="18.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_LessorDirectFinancingLeaseTermOfContract1_1523" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_RelatedPartyTransactionAxis_1489" xlink:to="us-gaap_RelatedPartyTransactionDomain_1490" />
    <link:definitionArc xlink:type="arc" order="19.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SummaryofSignificantAccountingPoliciesDetailsTable_1475" xlink:to="srt_ProductOrServiceAxis_1794" />
    <link:definitionArc xlink:type="arc" order="98.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_ProductOrServiceAxis_1794" xlink:to="srt_ProductsAndServicesDomain_1795" />
    <link:definitionArc xlink:type="arc" order="100.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_OperatingLeaseImpairmentLoss_1799" />
    <link:definitionArc xlink:type="arc" order="101.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_1800" />
    <link:definitionArc xlink:type="arc" order="102.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf_1801" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_MajorCustomersAxis_1497" xlink:to="srt_NameOfMajorCustomerDomain_1498" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_ForeignCurrencyExchangeRateTranslation1_1515" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_Deposits_1516" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_Cash_1517" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_ProvisionForDoubtfulAccounts_1519" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_1520" />
    <link:definitionArc xlink:type="arc" order="20.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_OtherIncome_1525" />
    <link:definitionArc xlink:type="arc" order="21.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_AccruedEmployeeBenefitsCurrent_1526" />
    <link:definitionArc xlink:type="arc" order="22.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_OperatingLeaseExpense_1527" />
    <link:definitionArc xlink:type="arc" order="24.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_ConcentrationRiskPercentage1_1529" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SummaryofSignificantAccountingPoliciesDetailsTable_1475" xlink:to="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionBySupplierAxis_1483" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SummaryofSignificantAccountingPoliciesDetailsTable_1475" xlink:to="us-gaap_ConcentrationRiskByTypeAxis_1492" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_ConcentrationRiskByTypeAxis_1492" xlink:to="us-gaap_ConcentrationRiskTypeDomain_1493" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SummaryofSignificantAccountingPoliciesDetailsTable_1475" xlink:to="srt_CurrencyAxis_1505" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SummaryofSignificantAccountingPoliciesDetailsTable_1475" xlink:to="srt_RangeAxis_1479" />
    <link:definitionArc xlink:type="arc" order="134.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_UnrecognizedTaxBenefits_34700" />
    <link:definitionArc xlink:type="arc" order="135.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ConcentrationRiskLineItems_1514" xlink:to="us-gaap_SegmentReportingOtherItemAmount_34701" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_RangeAxis_1479" xlink:to="srt_RangeMember_1480_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_CurrencyAxis_1505" xlink:to="currency_AllCurrenciesDomain_1506_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionBySupplierAxis_1483" xlink:to="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain_1484_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_ConcentrationRiskByBenchmarkAxis_1509" xlink:to="us-gaap_ConcentrationRiskBenchmarkDomain_1510_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_RelatedPartyTransactionAxis_1489" xlink:to="us-gaap_RelatedPartyTransactionDomain_1490_default" />
    <link:definitionArc xlink:type="arc" order="98.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_ProductOrServiceAxis_1794" xlink:to="srt_ProductsAndServicesDomain_1795_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_MajorCustomersAxis_1497" xlink:to="srt_NameOfMajorCustomerDomain_1498_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_ConcentrationRiskByTypeAxis_1492" xlink:to="us-gaap_ConcentrationRiskTypeDomain_1493_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/NatureofBusinessandOrganizationScheduleofConsolidatedFinancialStatementsDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_MelkwegHoldingsLimitedMelkwegCaymanMember" xlink:label="glxg_MelkwegHoldingsLimitedMelkwegCaymanMember_1279" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_MelkwegHoldingsBVILimitedMelkwegBVIMember" xlink:label="glxg_MelkwegHoldingsBVILimitedMelkwegBVIMember_1280" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_GalaxyPayrollServicesLimitedGalaxyPayrollHKMember" xlink:label="glxg_GalaxyPayrollServicesLimitedGalaxyPayrollHKMember_1281" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_GalaxyCorporateManagementConsultancyShenzhenLimitedGalaxyHRSZMember" xlink:label="glxg_GalaxyCorporateManagementConsultancyShenzhenLimitedGalaxyHRSZMember_1287" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_GalaxyPayrollGroupLimitedGalaxyPayrollBVIMember" xlink:label="glxg_GalaxyPayrollGroupLimitedGalaxyPayrollBVIMember_1278" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_GalaxyRecursosHumanosMacauLimitadaGalaxyHRMacauMember" xlink:label="glxg_GalaxyRecursosHumanosMacauLimitadaGalaxyHRMacauMember_1282" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_GalaxyPayrollTaiwanLimitedGalaxyPayrollTWMember" xlink:label="glxg_GalaxyPayrollTaiwanLimitedGalaxyPayrollTWMember_1283" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_GalaxyHumanResourcesLimitedGalaxyHRTWMember" xlink:label="glxg_GalaxyHumanResourcesLimitedGalaxyHRTWMember_1284" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_GalaxySolutionsPartnerLimitedGalaxySolutionsPartnerMember" xlink:label="glxg_GalaxySolutionsPartnerLimitedGalaxySolutionsPartnerMember_1285" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_GalaxyPayrollChinaLimitedGalaxyPayrollChinaMember" xlink:label="glxg_GalaxyPayrollChinaLimitedGalaxyPayrollChinaMember_1286" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:label="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_1288" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipState" xlink:label="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipState_1289" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipOwnershipPercentage" xlink:label="glxg_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipOwnershipPercentage_1290" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipBusinessPurpose" xlink:label="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipBusinessPurpose_1291" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesDomain" xlink:label="srt_ConsolidatedEntitiesDomain_1712" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:label="us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable_1276" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesAxis" xlink:label="srt_ConsolidatedEntitiesAxis_1277" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ScheduleOfConsolidatedFinancialStatementsAbstract" xlink:label="glxg_ScheduleOfConsolidatedFinancialStatementsAbstract_1275" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesDomain" xlink:label="srt_ConsolidatedEntitiesDomain_1712_default" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ConsolidatedEntitiesDomain_1712" xlink:to="glxg_MelkwegHoldingsLimitedMelkwegCaymanMember_1279" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ConsolidatedEntitiesDomain_1712" xlink:to="glxg_MelkwegHoldingsBVILimitedMelkwegBVIMember_1280" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ConsolidatedEntitiesDomain_1712" xlink:to="glxg_GalaxyPayrollServicesLimitedGalaxyPayrollHKMember_1281" />
    <link:definitionArc xlink:type="arc" order="21.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ConsolidatedEntitiesDomain_1712" xlink:to="glxg_GalaxyCorporateManagementConsultancyShenzhenLimitedGalaxyHRSZMember_1287" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ConsolidatedEntitiesDomain_1712" xlink:to="glxg_GalaxyPayrollGroupLimitedGalaxyPayrollBVIMember_1278" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ConsolidatedEntitiesDomain_1712" xlink:to="glxg_GalaxyRecursosHumanosMacauLimitadaGalaxyHRMacauMember_1282" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ConsolidatedEntitiesDomain_1712" xlink:to="glxg_GalaxyPayrollTaiwanLimitedGalaxyPayrollTWMember_1283" />
    <link:definitionArc xlink:type="arc" order="18.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ConsolidatedEntitiesDomain_1712" xlink:to="glxg_GalaxyHumanResourcesLimitedGalaxyHRTWMember_1284" />
    <link:definitionArc xlink:type="arc" order="19.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ConsolidatedEntitiesDomain_1712" xlink:to="glxg_GalaxySolutionsPartnerLimitedGalaxySolutionsPartnerMember_1285" />
    <link:definitionArc xlink:type="arc" order="20.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ConsolidatedEntitiesDomain_1712" xlink:to="glxg_GalaxyPayrollChinaLimitedGalaxyPayrollChinaMember_1286" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_1288" xlink:to="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipState_1289" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_1288" xlink:to="glxg_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipOwnershipPercentage_1290" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_1288" xlink:to="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipBusinessPurpose_1291" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_ConsolidatedEntitiesAxis_1277" xlink:to="srt_ConsolidatedEntitiesDomain_1712" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_1288" xlink:to="us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable_1276" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable_1276" xlink:to="srt_ConsolidatedEntitiesAxis_1277" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_ConsolidatedEntitiesAxis_1277" xlink:to="srt_ConsolidatedEntitiesDomain_1712_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/SummaryofSignificantAccountingPoliciesScheduleofEstimatedUsefulLivesDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseholdImprovementsMember" xlink:label="us-gaap_LeaseholdImprovementsMember_1296" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FurnitureAndFixturesMember" xlink:label="us-gaap_FurnitureAndFixturesMember_1297" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OfficeEquipmentMember" xlink:label="us-gaap_OfficeEquipmentMember_1298" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentLineItems" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_1299" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_1300" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_1713" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ScheduleOfPropertyAndEquipmentEstimatedUsefulLivesAbstract" xlink:label="glxg_ScheduleOfPropertyAndEquipmentEstimatedUsefulLivesAbstract_1293" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_SummaryofSignificantAccountingPoliciesScheduleofPropertyandEquipmentEstimatedUsefulLivesDetailsTable" xlink:label="glxg_SummaryofSignificantAccountingPoliciesScheduleofPropertyandEquipmentEstimatedUsefulLivesDetailsTable_1294" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_1295" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_1713_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PropertyPlantAndEquipmentTypeDomain_1713" xlink:to="us-gaap_LeaseholdImprovementsMember_1296" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PropertyPlantAndEquipmentTypeDomain_1713" xlink:to="us-gaap_FurnitureAndFixturesMember_1297" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PropertyPlantAndEquipmentTypeDomain_1713" xlink:to="us-gaap_OfficeEquipmentMember_1298" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems_1299" xlink:to="us-gaap_PropertyPlantAndEquipmentUsefulLife_1300" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_PropertyPlantAndEquipmentByTypeAxis_1295" xlink:to="us-gaap_PropertyPlantAndEquipmentTypeDomain_1713" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems_1299" xlink:to="glxg_SummaryofSignificantAccountingPoliciesScheduleofPropertyandEquipmentEstimatedUsefulLivesDetailsTable_1294" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SummaryofSignificantAccountingPoliciesScheduleofPropertyandEquipmentEstimatedUsefulLivesDetailsTable_1294" xlink:to="us-gaap_PropertyPlantAndEquipmentByTypeAxis_1295" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_PropertyPlantAndEquipmentByTypeAxis_1295" xlink:to="us-gaap_PropertyPlantAndEquipmentTypeDomain_1713_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/RevenuesScheduleofGroupsRevenuesDisaggregatedbyServiceLinesDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_EmploymentServicesMember" xlink:label="glxg_EmploymentServicesMember_1306" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PayrollOutsourcingServicesMember" xlink:label="glxg_PayrollOutsourcingServicesMember_1307" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ScheduleOfGroupSRevenuesDisaggregatedByServiceLinesAbstract" xlink:label="glxg_ScheduleOfGroupSRevenuesDisaggregatedByServiceLinesAbstract_1302" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_RevenuesScheduleofGroupsRevenuesDisaggregatedbyServiceLinesDetailsTable" xlink:label="glxg_RevenuesScheduleofGroupsRevenuesDisaggregatedbyServiceLinesDetailsTable_1303" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis" xlink:label="srt_ProductOrServiceAxis_1304" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain" xlink:label="srt_ProductsAndServicesDomain_1305" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueLineItems" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_1308" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues" xlink:label="us-gaap_Revenues_1310" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain" xlink:label="srt_ProductsAndServicesDomain_1305_default" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ProductsAndServicesDomain_1305" xlink:to="glxg_EmploymentServicesMember_1306" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ProductsAndServicesDomain_1305" xlink:to="glxg_PayrollOutsourcingServicesMember_1307" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_DisaggregationOfRevenueLineItems_1308" xlink:to="glxg_RevenuesScheduleofGroupsRevenuesDisaggregatedbyServiceLinesDetailsTable_1303" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_RevenuesScheduleofGroupsRevenuesDisaggregatedbyServiceLinesDetailsTable_1303" xlink:to="srt_ProductOrServiceAxis_1304" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_ProductOrServiceAxis_1304" xlink:to="srt_ProductsAndServicesDomain_1305" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_DisaggregationOfRevenueLineItems_1308" xlink:to="us-gaap_Revenues_1310" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_ProductOrServiceAxis_1304" xlink:to="srt_ProductsAndServicesDomain_1305_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/RevenuesScheduleofRevenuesDisaggregatedbyServiceLinesandGeographicLocationDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PRCMember" xlink:label="glxg_PRCMember_1318" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_EmploymentServicesMember" xlink:label="glxg_EmploymentServicesMember_1334" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PayrollOutsourcingServicesMember" xlink:label="glxg_PayrollOutsourcingServicesMember_1335" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ScheduleOfRevenuesDisaggregatedByServiceLinesAndGeographicLocationAbstract" xlink:label="glxg_ScheduleOfRevenuesDisaggregatedByServiceLinesAndGeographicLocationAbstract_1312" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_RevenuesScheduleofRevenuesDisaggregatedbyServiceLinesandGeographicLocationDetailsTable" xlink:label="glxg_RevenuesScheduleofRevenuesDisaggregatedbyServiceLinesandGeographicLocationDetailsTable_1313" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementGeographicalAxis" xlink:label="srt_StatementGeographicalAxis_1314" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain" xlink:label="srt_SegmentGeographicalDomain_1315" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_MOP" xlink:label="currency_MOP_1317" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_TW" xlink:label="country_TW_1319" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_SG" xlink:label="country_SG_1329" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_KRW" xlink:label="currency_KRW_1330" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_IT" xlink:label="country_IT_1331" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis" xlink:label="srt_ProductOrServiceAxis_1332" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain" xlink:label="srt_ProductsAndServicesDomain_1333" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_JP" xlink:label="country_JP_1320" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_TH" xlink:label="country_TH_1322" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_MY" xlink:label="country_MY_1323" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_VN" xlink:label="country_VN_1324" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_HK" xlink:label="country_HK_1316" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_BD" xlink:label="country_BD_1328" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_ID" xlink:label="country_ID_1326" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_AU" xlink:label="country_AU_1321" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_PH" xlink:label="country_PH_1327" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueLineItems" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_1336" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues" xlink:label="us-gaap_Revenues_1337" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_IN" xlink:label="country_IN_1325" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain" xlink:label="srt_SegmentGeographicalDomain_1315_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain" xlink:label="srt_ProductsAndServicesDomain_1333_default" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="glxg_PRCMember_1318" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ProductsAndServicesDomain_1333" xlink:to="glxg_EmploymentServicesMember_1334" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ProductsAndServicesDomain_1333" xlink:to="glxg_PayrollOutsourcingServicesMember_1335" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_DisaggregationOfRevenueLineItems_1336" xlink:to="glxg_RevenuesScheduleofRevenuesDisaggregatedbyServiceLinesandGeographicLocationDetailsTable_1313" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_RevenuesScheduleofRevenuesDisaggregatedbyServiceLinesandGeographicLocationDetailsTable_1313" xlink:to="srt_StatementGeographicalAxis_1314" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_StatementGeographicalAxis_1314" xlink:to="srt_SegmentGeographicalDomain_1315" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="currency_MOP_1317" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_TW_1319" />
    <link:definitionArc xlink:type="arc" order="24.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_SG_1329" />
    <link:definitionArc xlink:type="arc" order="25.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="currency_KRW_1330" />
    <link:definitionArc xlink:type="arc" order="26.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_IT_1331" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_RevenuesScheduleofRevenuesDisaggregatedbyServiceLinesandGeographicLocationDetailsTable_1313" xlink:to="srt_ProductOrServiceAxis_1332" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_ProductOrServiceAxis_1332" xlink:to="srt_ProductsAndServicesDomain_1333" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_JP_1320" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_TH_1322" />
    <link:definitionArc xlink:type="arc" order="18.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_MY_1323" />
    <link:definitionArc xlink:type="arc" order="19.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_VN_1324" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_HK_1316" />
    <link:definitionArc xlink:type="arc" order="23.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_BD_1328" />
    <link:definitionArc xlink:type="arc" order="21.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_ID_1326" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_AU_1321" />
    <link:definitionArc xlink:type="arc" order="22.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_PH_1327" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_DisaggregationOfRevenueLineItems_1336" xlink:to="us-gaap_Revenues_1337" />
    <link:definitionArc xlink:type="arc" order="20.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1315" xlink:to="country_IN_1325" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_StatementGeographicalAxis_1314" xlink:to="srt_SegmentGeographicalDomain_1315_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_ProductOrServiceAxis_1332" xlink:to="srt_ProductsAndServicesDomain_1333_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/TaxesDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PRCMember" xlink:label="glxg_PRCMember_34705" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TaxYearTwoThousandTwentySevenMember" xlink:label="glxg_TaxYearTwoThousandTwentySevenMember_34706" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TaxYearTwoThousandTwentyEightMember" xlink:label="glxg_TaxYearTwoThousandTwentyEightMember_34707" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TaxYearTwoThousandTwentyNineMember" xlink:label="glxg_TaxYearTwoThousandTwentyNineMember_34708" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TaxYearTwoThousandThirtyMember" xlink:label="glxg_TaxYearTwoThousandThirtyMember_34709" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TaxYearTwoThousandThirtyOneMember" xlink:label="glxg_TaxYearTwoThousandThirtyOneMember_34710" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TwotierProfitsTaxRatesMember" xlink:label="glxg_TwotierProfitsTaxRatesMember_1549" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureAbstract" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_1538" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TaxesDetailsTable" xlink:label="glxg_TaxesDetailsTable_1539" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementGeographicalAxis" xlink:label="srt_StatementGeographicalAxis_1540" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain" xlink:label="srt_SegmentGeographicalDomain_1541" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_HK" xlink:label="country_HK_1542" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_MOP" xlink:label="currency_MOP_1543" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_SZL" xlink:label="currency_SZL_1544" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_TW" xlink:label="country_TW_1545" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_US" xlink:label="country_US_1546" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLossCarryforwards" xlink:label="us-gaap_OperatingLossCarryforwards_1754" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TaxPeriodAxis" xlink:label="us-gaap_TaxPeriodAxis_34702" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TaxPeriodDomain" xlink:label="us-gaap_TaxPeriodDomain_34703" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxAuthorityNameAxis" xlink:label="us-gaap_IncomeTaxAuthorityNameAxis_1547" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxAuthorityNameDomain" xlink:label="us-gaap_IncomeTaxAuthorityNameDomain_1548" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxContingencyLineItems" xlink:label="us-gaap_IncomeTaxContingencyLineItems_1550" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit_1551" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_1552" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PercentageOfShareCapital" xlink:label="glxg_PercentageOfShareCapital_1553" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:label="us-gaap_IncomeTaxReconciliationTaxExemptIncome_1554" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:label="us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_1555" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionGainBeforeTax" xlink:label="us-gaap_ForeignCurrencyTransactionGainBeforeTax_1556" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic" xlink:label="us-gaap_EarningsPerShareBasic_1557" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted" xlink:label="us-gaap_EarningsPerShareDiluted_1558" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecognizedTaxBenefits" xlink:label="us-gaap_UnrecognizedTaxBenefits_1559" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain" xlink:label="srt_SegmentGeographicalDomain_1541_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TaxPeriodDomain" xlink:label="us-gaap_TaxPeriodDomain_34703_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxAuthorityNameDomain" xlink:label="us-gaap_IncomeTaxAuthorityNameDomain_1548_default" />
    <link:definitionArc xlink:type="arc" order="139.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1541" xlink:to="glxg_PRCMember_34705" />
    <link:definitionArc xlink:type="arc" order="140.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_TaxPeriodDomain_34703" xlink:to="glxg_TaxYearTwoThousandTwentySevenMember_34706" />
    <link:definitionArc xlink:type="arc" order="141.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_TaxPeriodDomain_34703" xlink:to="glxg_TaxYearTwoThousandTwentyEightMember_34707" />
    <link:definitionArc xlink:type="arc" order="142.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_TaxPeriodDomain_34703" xlink:to="glxg_TaxYearTwoThousandTwentyNineMember_34708" />
    <link:definitionArc xlink:type="arc" order="143.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_TaxPeriodDomain_34703" xlink:to="glxg_TaxYearTwoThousandThirtyMember_34709" />
    <link:definitionArc xlink:type="arc" order="144.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_TaxPeriodDomain_34703" xlink:to="glxg_TaxYearTwoThousandThirtyOneMember_34710" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxAuthorityNameDomain_1548" xlink:to="glxg_TwotierProfitsTaxRatesMember_1549" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="glxg_TaxesDetailsTable_1539" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_TaxesDetailsTable_1539" xlink:to="srt_StatementGeographicalAxis_1540" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_StatementGeographicalAxis_1540" xlink:to="srt_SegmentGeographicalDomain_1541" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1541" xlink:to="country_HK_1542" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1541" xlink:to="currency_MOP_1543" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1541" xlink:to="currency_SZL_1544" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1541" xlink:to="country_TW_1545" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1541" xlink:to="country_US_1546" />
    <link:definitionArc xlink:type="arc" order="62.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="us-gaap_OperatingLossCarryforwards_1754" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_TaxesDetailsTable_1539" xlink:to="us-gaap_TaxPeriodAxis_34702" />
    <link:definitionArc xlink:type="arc" order="137.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_TaxPeriodAxis_34702" xlink:to="us-gaap_TaxPeriodDomain_34703" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_TaxesDetailsTable_1539" xlink:to="us-gaap_IncomeTaxAuthorityNameAxis_1547" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_IncomeTaxAuthorityNameAxis_1547" xlink:to="us-gaap_IncomeTaxAuthorityNameDomain_1548" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="us-gaap_IncomeTaxExpenseBenefit_1551" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="us-gaap_EffectiveIncomeTaxRateContinuingOperations_1552" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="glxg_PercentageOfShareCapital_1553" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="us-gaap_IncomeTaxReconciliationTaxExemptIncome_1554" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_1555" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="us-gaap_ForeignCurrencyTransactionGainBeforeTax_1556" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="us-gaap_EarningsPerShareBasic_1557" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="us-gaap_EarningsPerShareDiluted_1558" />
    <link:definitionArc xlink:type="arc" order="18.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_IncomeTaxContingencyLineItems_1550" xlink:to="us-gaap_UnrecognizedTaxBenefits_1559" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_StatementGeographicalAxis_1540" xlink:to="srt_SegmentGeographicalDomain_1541_default" />
    <link:definitionArc xlink:type="arc" order="137.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_TaxPeriodAxis_34702" xlink:to="us-gaap_TaxPeriodDomain_34703_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_IncomeTaxAuthorityNameAxis_1547" xlink:to="us-gaap_IncomeTaxAuthorityNameDomain_1548_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/TaxesScheduleofIncomeTaxProvisionDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ForeignMember" xlink:label="glxg_ForeignMember_1396" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ScheduleOfIncomeTaxProvisionAbstract" xlink:label="glxg_ScheduleOfIncomeTaxProvisionAbstract_1391" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TaxesScheduleofIncomeTaxProvisionDetailsTable" xlink:label="glxg_TaxesScheduleofIncomeTaxProvisionDetailsTable_1392" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementGeographicalAxis" xlink:label="srt_StatementGeographicalAxis_1393" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain" xlink:label="srt_SegmentGeographicalDomain_1394" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_HK" xlink:label="country_HK_1395" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TaxesScheduleofIncomeTaxProvisionDetailsLineItems" xlink:label="glxg_TaxesScheduleofIncomeTaxProvisionDetailsLineItems_1397" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_1398" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit_1399" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit_1400" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain" xlink:label="srt_SegmentGeographicalDomain_1394_default" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1394" xlink:to="glxg_ForeignMember_1396" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="glxg_TaxesScheduleofIncomeTaxProvisionDetailsLineItems_1397" xlink:to="glxg_TaxesScheduleofIncomeTaxProvisionDetailsTable_1392" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_TaxesScheduleofIncomeTaxProvisionDetailsTable_1392" xlink:to="srt_StatementGeographicalAxis_1393" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_StatementGeographicalAxis_1393" xlink:to="srt_SegmentGeographicalDomain_1394" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_SegmentGeographicalDomain_1394" xlink:to="country_HK_1395" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="glxg_TaxesScheduleofIncomeTaxProvisionDetailsLineItems_1397" xlink:to="us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_1398" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_1398" xlink:to="us-gaap_CurrentIncomeTaxExpenseBenefit_1399" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_1398" xlink:to="us-gaap_IncomeTaxExpenseBenefit_1400" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_StatementGeographicalAxis_1393" xlink:to="srt_SegmentGeographicalDomain_1394_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/PropertyandEquipmentNetScheduleofPropertyandEquipmentDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseholdImprovementsMember" xlink:label="us-gaap_LeaseholdImprovementsMember_1369" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FurnitureAndFixturesMember" xlink:label="us-gaap_FurnitureAndFixturesMember_1370" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OfficeEquipmentMember" xlink:label="us-gaap_OfficeEquipmentMember_1371" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_1368" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentLineItems" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_1372" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentGross" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_1373" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_1374" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_1375" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ScheduleOfPropertyAndEquipmentAbstract" xlink:label="glxg_ScheduleOfPropertyAndEquipmentAbstract_1365" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_1366" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_1367" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_1368_default" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PropertyPlantAndEquipmentTypeDomain_1368" xlink:to="us-gaap_LeaseholdImprovementsMember_1369" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PropertyPlantAndEquipmentTypeDomain_1368" xlink:to="us-gaap_FurnitureAndFixturesMember_1370" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PropertyPlantAndEquipmentTypeDomain_1368" xlink:to="us-gaap_OfficeEquipmentMember_1371" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_PropertyPlantAndEquipmentByTypeAxis_1367" xlink:to="us-gaap_PropertyPlantAndEquipmentTypeDomain_1368" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems_1372" xlink:to="us-gaap_PropertyPlantAndEquipmentGross_1373" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems_1372" xlink:to="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_1374" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems_1372" xlink:to="us-gaap_PropertyPlantAndEquipmentNet_1375" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems_1372" xlink:to="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_1366" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_1366" xlink:to="us-gaap_PropertyPlantAndEquipmentByTypeAxis_1367" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_PropertyPlantAndEquipmentByTypeAxis_1367" xlink:to="us-gaap_PropertyPlantAndEquipmentTypeDomain_1368_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/ConsolidatedBalanceSheets" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember_1006" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember_1007" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepositsAssetsNoncurrent" xlink:label="us-gaap_DepositsAssetsNoncurrent_1018" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsNoncurrent" xlink:label="us-gaap_AssetsNoncurrent_1019" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets_1020" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_1021" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrentAbstract" xlink:label="us-gaap_LiabilitiesCurrentAbstract_1022" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent" xlink:label="us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent_1023" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableCurrent" xlink:label="us-gaap_AccountsPayableCurrent_1024" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TaxesPayableCurrent" xlink:label="us-gaap_TaxesPayableCurrent_1025" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue" xlink:label="us-gaap_CommonStockValue_1034" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteSubscriptionsReceivable" xlink:label="us-gaap_StockholdersEquityNoteSubscriptionsReceivable_1035" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_SharesReservedForIssuance" xlink:label="glxg_SharesReservedForIssuance_1036" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalCommonStock" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_1037" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_1038" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_1039" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrentAbstract" xlink:label="us-gaap_AssetsCurrentAbstract_1010" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Cash" xlink:label="us-gaap_Cash_1011" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNetCurrent" xlink:label="us-gaap_AccountsReceivableNetCurrent_1012" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_1013" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent" xlink:label="us-gaap_AssetsCurrent_1014" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_1015" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAsset" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_1016" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrent" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_1026" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent" xlink:label="us-gaap_LiabilitiesCurrent_1027" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesAbstract" xlink:label="us-gaap_OtherLiabilitiesAbstract_1028" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_1029" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesNoncurrent" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_1030" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities_1031" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies" xlink:label="us-gaap_CommitmentsAndContingencies_1032" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityAbstract" xlink:label="us-gaap_StockholdersEquityAbstract_1033" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract" xlink:label="us-gaap_AssetsAbstract_1009" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity_1040" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_1041" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_1002" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable_1003" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis_1004" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1005" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems_1008" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1005_default" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1005" xlink:to="us-gaap_CommonClassAMember_1006" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1005" xlink:to="us-gaap_CommonClassBMember_1007" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsCurrentAbstract_1010" xlink:to="us-gaap_DepositsAssetsNoncurrent_1018" />
    <link:definitionArc xlink:type="arc" order="18.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsCurrentAbstract_1010" xlink:to="us-gaap_AssetsNoncurrent_1019" />
    <link:definitionArc xlink:type="arc" order="19.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsCurrentAbstract_1010" xlink:to="us-gaap_Assets_1020" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1008" xlink:to="us-gaap_LiabilitiesAndStockholdersEquityAbstract_1021" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract_1021" xlink:to="us-gaap_LiabilitiesCurrentAbstract_1022" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_LiabilitiesCurrentAbstract_1022" xlink:to="us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent_1023" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_LiabilitiesCurrentAbstract_1022" xlink:to="us-gaap_AccountsPayableCurrent_1024" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_LiabilitiesCurrentAbstract_1022" xlink:to="us-gaap_TaxesPayableCurrent_1025" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StockholdersEquityAbstract_1033" xlink:to="us-gaap_CommonStockValue_1034" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StockholdersEquityAbstract_1033" xlink:to="us-gaap_StockholdersEquityNoteSubscriptionsReceivable_1035" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StockholdersEquityAbstract_1033" xlink:to="glxg_SharesReservedForIssuance_1036" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StockholdersEquityAbstract_1033" xlink:to="us-gaap_AdditionalPaidInCapitalCommonStock_1037" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StockholdersEquityAbstract_1033" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit_1038" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StockholdersEquityAbstract_1033" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_1039" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsAbstract_1009" xlink:to="us-gaap_AssetsCurrentAbstract_1010" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsCurrentAbstract_1010" xlink:to="us-gaap_Cash_1011" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsCurrentAbstract_1010" xlink:to="us-gaap_AccountsReceivableNetCurrent_1012" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsCurrentAbstract_1010" xlink:to="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_1013" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsCurrentAbstract_1010" xlink:to="us-gaap_AssetsCurrent_1014" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsCurrentAbstract_1010" xlink:to="us-gaap_PropertyPlantAndEquipmentNet_1015" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_AssetsCurrentAbstract_1010" xlink:to="us-gaap_OperatingLeaseRightOfUseAsset_1016" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_LiabilitiesCurrentAbstract_1022" xlink:to="us-gaap_OperatingLeaseLiabilityCurrent_1026" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_LiabilitiesCurrentAbstract_1022" xlink:to="us-gaap_LiabilitiesCurrent_1027" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract_1021" xlink:to="us-gaap_OtherLiabilitiesAbstract_1028" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OtherLiabilitiesAbstract_1028" xlink:to="us-gaap_OperatingLeaseLiabilityNoncurrent_1029" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OtherLiabilitiesAbstract_1028" xlink:to="us-gaap_OtherLiabilitiesNoncurrent_1030" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OtherLiabilitiesAbstract_1028" xlink:to="us-gaap_Liabilities_1031" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1008" xlink:to="us-gaap_CommitmentsAndContingencies_1032" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1008" xlink:to="us-gaap_StockholdersEquityAbstract_1033" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1008" xlink:to="us-gaap_AssetsAbstract_1009" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StockholdersEquityAbstract_1033" xlink:to="us-gaap_StockholdersEquity_1040" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StockholdersEquityAbstract_1033" xlink:to="us-gaap_LiabilitiesAndStockholdersEquity_1041" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_StatementLineItems_1008" xlink:to="us-gaap_StatementTable_1003" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_StatementTable_1003" xlink:to="us-gaap_StatementClassOfStockAxis_1004" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementClassOfStockAxis_1004" xlink:to="us-gaap_ClassOfStockDomain_1005" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementClassOfStockAxis_1004" xlink:to="us-gaap_ClassOfStockDomain_1005_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/ShareBasedCompensationDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TwoThousandTwentyFiveShareIncentivePlanMember" xlink:label="glxg_TwoThousandTwentyFiveShareIncentivePlanMember_1617" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember_1620" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember" xlink:label="srt_RangeMember_1776" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember" xlink:label="srt_MinimumMember_1777" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember" xlink:label="srt_MaximumMember_1778" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember" xlink:label="us-gaap_CommonStockMember_34687" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_1780" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_1781" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_1807" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameDomain" xlink:label="us-gaap_PlanNameDomain_1616" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis_1618" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1619" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_1625" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Cash" xlink:label="us-gaap_Cash_1808" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_1817" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_Share-BasedCompensationArrangementByShare-BasedPaymentAwardOptionsNonvestedSharesWeightedAverageGrantDateFairValue" xlink:label="glxg_Share-BasedCompensationArrangementByShare-BasedPaymentAwardOptionsNonvestedSharesWeightedAverageGrantDateFairValue_34711" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_34712" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_Share-BasedCompensationArrangementByShare-BasedPaymentAwardOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:label="glxg_Share-BasedCompensationArrangementByShare-BasedPaymentAwardOptionsNonvestedWeightedAverageGrantDateFairValue_34713" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis_1775" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityReverseStockSplit" xlink:label="us-gaap_StockholdersEquityReverseStockSplit_1779" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationAbstract" xlink:label="us-gaap_ShareBasedCompensationAbstract_1613" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ShareBasedCompensationDetailsTable" xlink:label="glxg_ShareBasedCompensationDetailsTable_1614" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameAxis" xlink:label="us-gaap_PlanNameAxis_1615" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis" xlink:label="us-gaap_StatementEquityComponentsAxis_34685" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain_34686" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllocatedShareBasedCompensationExpense" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_1626" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember" xlink:label="srt_RangeMember_1776_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameDomain" xlink:label="us-gaap_PlanNameDomain_1616_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1619_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain_34686_default" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PlanNameDomain_1616" xlink:to="glxg_TwoThousandTwentyFiveShareIncentivePlanMember_1617" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1619" xlink:to="us-gaap_CommonClassAMember_1620" />
    <link:definitionArc xlink:type="arc" order="83.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_RangeAxis_1775" xlink:to="srt_RangeMember_1776" />
    <link:definitionArc xlink:type="arc" order="84.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_RangeMember_1776" xlink:to="srt_MinimumMember_1777" />
    <link:definitionArc xlink:type="arc" order="85.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_RangeMember_1776" xlink:to="srt_MaximumMember_1778" />
    <link:definitionArc xlink:type="arc" order="123.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_EquityComponentDomain_34686" xlink:to="us-gaap_CommonStockMember_34687" />
    <link:definitionArc xlink:type="arc" order="87.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_1780" />
    <link:definitionArc xlink:type="arc" order="88.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_1781" />
    <link:definitionArc xlink:type="arc" order="104.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_1807" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_PlanNameAxis_1615" xlink:to="us-gaap_PlanNameDomain_1616" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_ShareBasedCompensationDetailsTable_1614" xlink:to="us-gaap_StatementClassOfStockAxis_1618" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementClassOfStockAxis_1618" xlink:to="us-gaap_ClassOfStockDomain_1619" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_1625" />
    <link:definitionArc xlink:type="arc" order="105.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="us-gaap_Cash_1808" />
    <link:definitionArc xlink:type="arc" order="110.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_1817" />
    <link:definitionArc xlink:type="arc" order="145.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="glxg_Share-BasedCompensationArrangementByShare-BasedPaymentAwardOptionsNonvestedSharesWeightedAverageGrantDateFairValue_34711" />
    <link:definitionArc xlink:type="arc" order="146.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_34712" />
    <link:definitionArc xlink:type="arc" order="147.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="glxg_Share-BasedCompensationArrangementByShare-BasedPaymentAwardOptionsNonvestedWeightedAverageGrantDateFairValue_34713" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_ShareBasedCompensationDetailsTable_1614" xlink:to="srt_RangeAxis_1775" />
    <link:definitionArc xlink:type="arc" order="86.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="us-gaap_StockholdersEquityReverseStockSplit_1779" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="glxg_ShareBasedCompensationDetailsTable_1614" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_ShareBasedCompensationDetailsTable_1614" xlink:to="us-gaap_PlanNameAxis_1615" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_ShareBasedCompensationDetailsTable_1614" xlink:to="us-gaap_StatementEquityComponentsAxis_34685" />
    <link:definitionArc xlink:type="arc" order="122.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementEquityComponentsAxis_34685" xlink:to="us-gaap_EquityComponentDomain_34686" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_1624" xlink:to="us-gaap_AllocatedShareBasedCompensationExpense_1626" />
    <link:definitionArc xlink:type="arc" order="83.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_RangeAxis_1775" xlink:to="srt_RangeMember_1776_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_PlanNameAxis_1615" xlink:to="us-gaap_PlanNameDomain_1616_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementClassOfStockAxis_1618" xlink:to="us-gaap_ClassOfStockDomain_1619_default" />
    <link:definitionArc xlink:type="arc" order="122.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementEquityComponentsAxis_34685" xlink:to="us-gaap_EquityComponentDomain_34686_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/DocumentAndEntityInformation" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_BusinessContactMember" xlink:label="dei_BusinessContactMember_1663" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember_1666" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember_1667" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityWellKnownSeasonedIssuer" xlink:label="dei_EntityWellKnownSeasonedIssuer_1695" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityVoluntaryFilers" xlink:label="dei_EntityVoluntaryFilers_1696" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCurrentReportingStatus" xlink:label="dei_EntityCurrentReportingStatus_1697" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent" xlink:label="dei_EntityInteractiveDataCurrent_1698" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory" xlink:label="dei_EntityFilerCategory_1699" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany" xlink:label="dei_EntityEmergingGrowthCompany_1700" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityExTransitionPeriod" xlink:label="dei_EntityExTransitionPeriod_1701" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus" xlink:label="dei_DocumentFiscalPeriodFocus_1711" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown" xlink:label="dei_EntityAddressCityOrTown_1684" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCountry" xlink:label="dei_EntityAddressCountry_1685" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_ContactPersonnelName" xlink:label="dei_ContactPersonnelName_1686" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince" xlink:label="dei_EntityAddressStateOrProvince_1687" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode" xlink:label="dei_EntityAddressPostalZipCode_1688" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode" xlink:label="dei_CityAreaCode_1689" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1" xlink:label="dei_EntityAddressAddressLine1_1681" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine2" xlink:label="dei_EntityAddressAddressLine2_1682" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine3" xlink:label="dei_EntityAddressAddressLine3_1683" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName" xlink:label="dei_SecurityExchangeName_1693" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding" xlink:label="dei_EntityCommonStockSharesOutstanding_1694" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_DocumentAndEntityInformationAbstract" xlink:label="glxg_DocumentAndEntityInformationAbstract_1659" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationTable" xlink:label="dei_DocumentInformationTable_1660" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressesAddressTypeAxis" xlink:label="dei_EntityAddressesAddressTypeAxis_1661" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AddressTypeDomain" xlink:label="dei_AddressTypeDomain_1662" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis_1664" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1665" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus" xlink:label="dei_DocumentFiscalYearFocus_1675" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport" xlink:label="dei_DocumentTransitionReport_1676" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentShellCompanyReport" xlink:label="dei_DocumentShellCompanyReport_1677" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber" xlink:label="dei_EntityFileNumber_1678" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName_1679" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode" xlink:label="dei_EntityIncorporationStateCountryCode_1680" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag" xlink:label="dei_AmendmentFlag_1710" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType" xlink:label="dei_DocumentType_1670" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentRegistrationStatement" xlink:label="dei_DocumentRegistrationStatement_1671" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber" xlink:label="dei_LocalPhoneNumber_1690" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle" xlink:label="dei_Security12bTitle_1691" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol" xlink:label="dei_TradingSymbol_1692" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_IcfrAuditorAttestationFlag" xlink:label="dei_IcfrAuditorAttestationFlag_1702" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFinStmtErrorCorrectionFlag" xlink:label="dei_DocumentFinStmtErrorCorrectionFlag_1703" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentAccountingStandard" xlink:label="dei_DocumentAccountingStandard_1704" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany" xlink:label="dei_EntityShellCompany_1705" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationLineItems" xlink:label="dei_DocumentInformationLineItems_1668" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey" xlink:label="dei_EntityCentralIndexKey_1669" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentAnnualReport" xlink:label="dei_DocumentAnnualReport_1672" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate" xlink:label="dei_CurrentFiscalYearEndDate_1673" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate" xlink:label="dei_DocumentPeriodEndDate_1674" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AddressTypeDomain" xlink:label="dei_AddressTypeDomain_1662_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1665_default" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_AddressTypeDomain_1662" xlink:to="dei_BusinessContactMember_1663" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1665" xlink:to="us-gaap_CommonClassAMember_1666" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1665" xlink:to="us-gaap_CommonClassBMember_1667" />
    <link:definitionArc xlink:type="arc" order="36.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityWellKnownSeasonedIssuer_1695" />
    <link:definitionArc xlink:type="arc" order="37.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityVoluntaryFilers_1696" />
    <link:definitionArc xlink:type="arc" order="38.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityCurrentReportingStatus_1697" />
    <link:definitionArc xlink:type="arc" order="39.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityInteractiveDataCurrent_1698" />
    <link:definitionArc xlink:type="arc" order="40.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityFilerCategory_1699" />
    <link:definitionArc xlink:type="arc" order="41.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityEmergingGrowthCompany_1700" />
    <link:definitionArc xlink:type="arc" order="42.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityExTransitionPeriod_1701" />
    <link:definitionArc xlink:type="arc" order="52.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentFiscalPeriodFocus_1711" />
    <link:definitionArc xlink:type="arc" order="25.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityAddressCityOrTown_1684" />
    <link:definitionArc xlink:type="arc" order="26.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityAddressCountry_1685" />
    <link:definitionArc xlink:type="arc" order="27.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_ContactPersonnelName_1686" />
    <link:definitionArc xlink:type="arc" order="28.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityAddressStateOrProvince_1687" />
    <link:definitionArc xlink:type="arc" order="29.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityAddressPostalZipCode_1688" />
    <link:definitionArc xlink:type="arc" order="30.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_CityAreaCode_1689" />
    <link:definitionArc xlink:type="arc" order="22.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityAddressAddressLine1_1681" />
    <link:definitionArc xlink:type="arc" order="23.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityAddressAddressLine2_1682" />
    <link:definitionArc xlink:type="arc" order="24.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityAddressAddressLine3_1683" />
    <link:definitionArc xlink:type="arc" order="34.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_SecurityExchangeName_1693" />
    <link:definitionArc xlink:type="arc" order="35.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityCommonStockSharesOutstanding_1694" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentInformationTable_1660" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="dei_DocumentInformationTable_1660" xlink:to="dei_EntityAddressesAddressTypeAxis_1661" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="dei_EntityAddressesAddressTypeAxis_1661" xlink:to="dei_AddressTypeDomain_1662" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="dei_DocumentInformationTable_1660" xlink:to="us-gaap_StatementClassOfStockAxis_1664" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementClassOfStockAxis_1664" xlink:to="us-gaap_ClassOfStockDomain_1665" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentFiscalYearFocus_1675" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentTransitionReport_1676" />
    <link:definitionArc xlink:type="arc" order="18.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentShellCompanyReport_1677" />
    <link:definitionArc xlink:type="arc" order="19.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityFileNumber_1678" />
    <link:definitionArc xlink:type="arc" order="20.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityRegistrantName_1679" />
    <link:definitionArc xlink:type="arc" order="21.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityIncorporationStateCountryCode_1680" />
    <link:definitionArc xlink:type="arc" order="51.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_AmendmentFlag_1710" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentType_1670" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentRegistrationStatement_1671" />
    <link:definitionArc xlink:type="arc" order="31.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_LocalPhoneNumber_1690" />
    <link:definitionArc xlink:type="arc" order="32.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_Security12bTitle_1691" />
    <link:definitionArc xlink:type="arc" order="33.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_TradingSymbol_1692" />
    <link:definitionArc xlink:type="arc" order="43.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_IcfrAuditorAttestationFlag_1702" />
    <link:definitionArc xlink:type="arc" order="44.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentFinStmtErrorCorrectionFlag_1703" />
    <link:definitionArc xlink:type="arc" order="45.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentAccountingStandard_1704" />
    <link:definitionArc xlink:type="arc" order="46.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityShellCompany_1705" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_EntityCentralIndexKey_1669" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentAnnualReport_1672" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_CurrentFiscalYearEndDate_1673" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="dei_DocumentInformationLineItems_1668" xlink:to="dei_DocumentPeriodEndDate_1674" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="dei_EntityAddressesAddressTypeAxis_1661" xlink:to="dei_AddressTypeDomain_1662_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementClassOfStockAxis_1664" xlink:to="us-gaap_ClassOfStockDomain_1665_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/RelatedPartyTransactionsScheduleofTransactionswithRelatedPartiesDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_NoahTrustAsiaLimitedMember" xlink:label="glxg_NoahTrustAsiaLimitedMember_1434" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_NebulaThreeHundredAndSixtyServicesLimitedMember" xlink:label="glxg_NebulaThreeHundredAndSixtyServicesLimitedMember_1435" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_Nebula360ServicesLimitedOneMember" xlink:label="glxg_Nebula360ServicesLimitedOneMember_1755" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain_1715" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDescriptionOfTransaction" xlink:label="us-gaap_RelatedPartyTransactionDescriptionOfTransaction_1438" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction_1439" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ScheduleOfTransactionsWithRelatedPartiesAbstract" xlink:label="glxg_ScheduleOfTransactionsWithRelatedPartiesAbstract_1431" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1432" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_1433" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:label="us-gaap_RelatedPartyTransactionLineItems_1436" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_RelatedPartyTransactionRelationship" xlink:label="glxg_RelatedPartyTransactionRelationship_1437" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain_1715_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyDomain_1715" xlink:to="glxg_NoahTrustAsiaLimitedMember_1434" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyDomain_1715" xlink:to="glxg_NebulaThreeHundredAndSixtyServicesLimitedMember_1435" />
    <link:definitionArc xlink:type="arc" order="63.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyDomain_1715" xlink:to="glxg_Nebula360ServicesLimitedOneMember_1755" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_1433" xlink:to="us-gaap_RelatedPartyDomain_1715" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems_1436" xlink:to="us-gaap_RelatedPartyTransactionDescriptionOfTransaction_1438" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems_1436" xlink:to="us-gaap_RelatedPartyTransactionAmountsOfTransaction_1439" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_RelatedPartyTransactionLineItems_1436" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1432" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_1432" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_1433" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RelatedPartyTransactionLineItems_1436" xlink:to="glxg_RelatedPartyTransactionRelationship_1437" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_1433" xlink:to="us-gaap_RelatedPartyDomain_1715_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/SubsequentEventsDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember_1639" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventMember" xlink:label="us-gaap_SubsequentEventMember_1646" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TwoThousandTwentyFiveShareIncentivePlanMember" xlink:label="glxg_TwoThousandTwentyFiveShareIncentivePlanMember_1820" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TwoThousandTwentySixPIPETransactionMember" xlink:label="glxg_TwoThousandTwentySixPIPETransactionMember_34691" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioForecastMember" xlink:label="srt_ScenarioForecastMember_34695" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain_1717" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis_1637" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1638" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsAbstract" xlink:label="us-gaap_SubsequentEventsAbstract_1629" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_SubsequentEventsDetailsTable" xlink:label="glxg_SubsequentEventsDetailsTable_1630" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeAxis" xlink:label="us-gaap_SubsequentEventTypeAxis_1645" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventLineItems" xlink:label="us-gaap_SubsequentEventLineItems_1647" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameAxis" xlink:label="us-gaap_PlanNameAxis_1818" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameDomain" xlink:label="us-gaap_PlanNameDomain_1819" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_1821" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteSubscriptionsReceivable" xlink:label="us-gaap_StockholdersEquityNoteSubscriptionsReceivable_34690" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementScenarioAxis" xlink:label="srt_StatementScenarioAxis_34693" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioUnspecifiedDomain" xlink:label="srt_ScenarioUnspecifiedDomain_34694" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain_1717_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1638_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameDomain" xlink:label="us-gaap_PlanNameDomain_1819_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioUnspecifiedDomain" xlink:label="srt_ScenarioUnspecifiedDomain_34694_default" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1638" xlink:to="us-gaap_CommonClassAMember_1639" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsequentEventTypeDomain_1717" xlink:to="us-gaap_SubsequentEventMember_1646" />
    <link:definitionArc xlink:type="arc" order="113.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PlanNameDomain_1819" xlink:to="glxg_TwoThousandTwentyFiveShareIncentivePlanMember_1820" />
    <link:definitionArc xlink:type="arc" order="126.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PlanNameDomain_1819" xlink:to="glxg_TwoThousandTwentySixPIPETransactionMember_34691" />
    <link:definitionArc xlink:type="arc" order="129.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ScenarioUnspecifiedDomain_34694" xlink:to="srt_ScenarioForecastMember_34695" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_SubsequentEventTypeAxis_1645" xlink:to="us-gaap_SubsequentEventTypeDomain_1717" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SubsequentEventsDetailsTable_1630" xlink:to="us-gaap_StatementClassOfStockAxis_1637" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementClassOfStockAxis_1637" xlink:to="us-gaap_ClassOfStockDomain_1638" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_SubsequentEventLineItems_1647" xlink:to="glxg_SubsequentEventsDetailsTable_1630" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SubsequentEventsDetailsTable_1630" xlink:to="us-gaap_SubsequentEventTypeAxis_1645" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SubsequentEventsDetailsTable_1630" xlink:to="us-gaap_PlanNameAxis_1818" />
    <link:definitionArc xlink:type="arc" order="112.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_PlanNameAxis_1818" xlink:to="us-gaap_PlanNameDomain_1819" />
    <link:definitionArc xlink:type="arc" order="114.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsequentEventLineItems_1647" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_1821" />
    <link:definitionArc xlink:type="arc" order="115.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SubsequentEventLineItems_1647" xlink:to="us-gaap_StockholdersEquityNoteSubscriptionsReceivable_34690" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_SubsequentEventsDetailsTable_1630" xlink:to="srt_StatementScenarioAxis_34693" />
    <link:definitionArc xlink:type="arc" order="128.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_StatementScenarioAxis_34693" xlink:to="srt_ScenarioUnspecifiedDomain_34694" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_SubsequentEventTypeAxis_1645" xlink:to="us-gaap_SubsequentEventTypeDomain_1717_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementClassOfStockAxis_1637" xlink:to="us-gaap_ClassOfStockDomain_1638_default" />
    <link:definitionArc xlink:type="arc" order="112.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_PlanNameAxis_1818" xlink:to="us-gaap_PlanNameDomain_1819_default" />
    <link:definitionArc xlink:type="arc" order="128.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_StatementScenarioAxis_34693" xlink:to="srt_ScenarioUnspecifiedDomain_34694_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/ConsolidatedBalanceSheetsParentheticals" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember_1047" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember_1048" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_1043" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable_1044" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis_1045" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1046" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems_1049" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_1050" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued_1052" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding_1053" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_1718" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityReverseStockSplit" xlink:label="us-gaap_StockholdersEquityReverseStockSplit_1813" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorizedUnlimited" xlink:label="us-gaap_CommonStockSharesAuthorizedUnlimited_1051" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1046_default" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1046" xlink:to="us-gaap_CommonClassAMember_1047" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1046" xlink:to="us-gaap_CommonClassBMember_1048" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_StatementLineItems_1049" xlink:to="us-gaap_StatementTable_1044" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_StatementTable_1044" xlink:to="us-gaap_StatementClassOfStockAxis_1045" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementClassOfStockAxis_1045" xlink:to="us-gaap_ClassOfStockDomain_1046" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1049" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare_1050" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1049" xlink:to="us-gaap_CommonStockSharesIssued_1052" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1049" xlink:to="us-gaap_CommonStockSharesOutstanding_1053" />
    <link:definitionArc xlink:type="arc" order="53.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1049" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_1718" />
    <link:definitionArc xlink:type="arc" order="109.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1049" xlink:to="us-gaap_StockholdersEquityReverseStockSplit_1813" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1049" xlink:to="us-gaap_CommonStockSharesAuthorizedUnlimited_1051" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementClassOfStockAxis_1045" xlink:to="us-gaap_ClassOfStockDomain_1046_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/EquityDetails" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IPOMember" xlink:label="us-gaap_IPOMember_1569" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ReDesignationOfOrdinarySharesMember" xlink:label="glxg_ReDesignationOfOrdinarySharesMember_1572" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember_1573" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember_1574" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_TwoThousandTwentyFiveShareIncentivePlanMember" xlink:label="glxg_TwoThousandTwentyFiveShareIncentivePlanMember_1760" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PostSplitClassAOrdinarySharesMember" xlink:label="glxg_PostSplitClassAOrdinarySharesMember_1768" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PreSplitClassAOrdinarySharesMember" xlink:label="glxg_PreSplitClassAOrdinarySharesMember_1769" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember" xlink:label="srt_RangeMember_1576" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember" xlink:label="srt_MinimumMember_1577" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember" xlink:label="srt_MaximumMember_1578" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember" xlink:label="us-gaap_CommonStockMember_1584" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_EmployeeShareOwnershipPlanMember" xlink:label="glxg_EmployeeShareOwnershipPlanMember_1587" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorizedUnlimited" xlink:label="us-gaap_CommonStockSharesAuthorizedUnlimited_1792" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_1599" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_1601" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_1602" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockOtherSharesOutstanding" xlink:label="us-gaap_CommonStockOtherSharesOutstanding_1603" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesOther" xlink:label="us-gaap_StockIssuedDuringPeriodSharesOther_1604" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Dividends" xlink:label="us-gaap_Dividends_1605" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDividends" xlink:label="us-gaap_PaymentsOfDividends_1606" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityAbstract" xlink:label="us-gaap_EquityAbstract_1565" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_EquityDetailsTable" xlink:label="glxg_EquityDetailsTable_1566" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_1567" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_1568" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis_1570" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1571" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis_1575" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CurrencyAxis" xlink:label="srt_CurrencyAxis_1809" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_AllCurrenciesDomain" xlink:label="currency_AllCurrenciesDomain_1810" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_HKD" xlink:label="currency_HKD_1811" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityReverseStockSplit" xlink:label="us-gaap_StockholdersEquityReverseStockSplit_1757" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_IssuanceOfOrdinaryShare" xlink:label="glxg_IssuanceOfOrdinaryShare_1762" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesIssuedPricePerShare" xlink:label="us-gaap_SharesIssuedPricePerShare_1763" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PercentageOfClosingPrice" xlink:label="glxg_PercentageOfClosingPrice_1764" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_ProceedFromPIPEInvestors" xlink:label="glxg_ProceedFromPIPEInvestors_1765" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PercentageOfRepaymentOfTotalOutstanding" xlink:label="glxg_PercentageOfRepaymentOfTotalOutstanding_1766" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteSubscriptionsReceivable" xlink:label="us-gaap_StockholdersEquityNoteSubscriptionsReceivable_1767" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOwnershipPlanESOPSharesInESOP" xlink:label="us-gaap_EmployeeStockOwnershipPlanESOPSharesInESOP_1770" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedNumberOfShares" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedNumberOfShares_1771" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_1772" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_1773" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis" xlink:label="us-gaap_StatementEquityComponentsAxis_1582" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockLineItems" xlink:label="us-gaap_ClassOfStockLineItems_1591" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued_1592" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_1593" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding_1594" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockVotingRights" xlink:label="us-gaap_CommonStockVotingRights_1595" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_1597" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockPricePerShare" xlink:label="us-gaap_SaleOfStockPricePerShare_1598" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsPayableAmountPerShare" xlink:label="us-gaap_DividendsPayableAmountPerShare_1607" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsPayableCurrent" xlink:label="us-gaap_DividendsPayableCurrent_1608" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain_1583" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameAxis" xlink:label="us-gaap_PlanNameAxis_1585" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameDomain" xlink:label="us-gaap_PlanNameDomain_1586" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember" xlink:label="srt_RangeMember_1576_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_1568_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1571_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/currency/2026/currency-2026.xsd#currency_AllCurrenciesDomain" xlink:label="currency_AllCurrenciesDomain_1810_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain_1583_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameDomain" xlink:label="us-gaap_PlanNameDomain_1586_default" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain_1568" xlink:to="us-gaap_IPOMember_1569" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1571" xlink:to="glxg_ReDesignationOfOrdinarySharesMember_1572" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1571" xlink:to="us-gaap_CommonClassBMember_1573" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1571" xlink:to="us-gaap_CommonClassAMember_1574" />
    <link:definitionArc xlink:type="arc" order="67.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PlanNameDomain_1586" xlink:to="glxg_TwoThousandTwentyFiveShareIncentivePlanMember_1760" />
    <link:definitionArc xlink:type="arc" order="75.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1571" xlink:to="glxg_PostSplitClassAOrdinarySharesMember_1768" />
    <link:definitionArc xlink:type="arc" order="76.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1571" xlink:to="glxg_PreSplitClassAOrdinarySharesMember_1769" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_RangeAxis_1575" xlink:to="srt_RangeMember_1576" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_RangeMember_1576" xlink:to="srt_MinimumMember_1577" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_RangeMember_1576" xlink:to="srt_MaximumMember_1578" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_EquityComponentDomain_1583" xlink:to="us-gaap_CommonStockMember_1584" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_PlanNameDomain_1586" xlink:to="glxg_EmployeeShareOwnershipPlanMember_1587" />
    <link:definitionArc xlink:type="arc" order="95.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_CommonStockSharesAuthorizedUnlimited_1792" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_ProceedsFromIssuanceInitialPublicOffering_1599" />
    <link:definitionArc xlink:type="arc" order="19.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_1601" />
    <link:definitionArc xlink:type="arc" order="20.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_1602" />
    <link:definitionArc xlink:type="arc" order="21.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_CommonStockOtherSharesOutstanding_1603" />
    <link:definitionArc xlink:type="arc" order="22.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_StockIssuedDuringPeriodSharesOther_1604" />
    <link:definitionArc xlink:type="arc" order="23.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_Dividends_1605" />
    <link:definitionArc xlink:type="arc" order="24.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_PaymentsOfDividends_1606" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="glxg_EquityDetailsTable_1566" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_EquityDetailsTable_1566" xlink:to="us-gaap_SubsidiarySaleOfStockAxis_1567" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_SubsidiarySaleOfStockAxis_1567" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain_1568" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_EquityDetailsTable_1566" xlink:to="us-gaap_StatementClassOfStockAxis_1570" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementClassOfStockAxis_1570" xlink:to="us-gaap_ClassOfStockDomain_1571" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_EquityDetailsTable_1566" xlink:to="srt_RangeAxis_1575" />
    <link:definitionArc xlink:type="arc" order="18.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_EquityDetailsTable_1566" xlink:to="srt_CurrencyAxis_1809" />
    <link:definitionArc xlink:type="arc" order="107.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_CurrencyAxis_1809" xlink:to="currency_AllCurrenciesDomain_1810" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="currency_AllCurrenciesDomain_1810" xlink:to="currency_HKD_1811" />
    <link:definitionArc xlink:type="arc" order="64.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_StockholdersEquityReverseStockSplit_1757" />
    <link:definitionArc xlink:type="arc" order="69.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="glxg_IssuanceOfOrdinaryShare_1762" />
    <link:definitionArc xlink:type="arc" order="70.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_SharesIssuedPricePerShare_1763" />
    <link:definitionArc xlink:type="arc" order="71.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="glxg_PercentageOfClosingPrice_1764" />
    <link:definitionArc xlink:type="arc" order="72.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="glxg_ProceedFromPIPEInvestors_1765" />
    <link:definitionArc xlink:type="arc" order="73.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="glxg_PercentageOfRepaymentOfTotalOutstanding_1766" />
    <link:definitionArc xlink:type="arc" order="74.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_StockholdersEquityNoteSubscriptionsReceivable_1767" />
    <link:definitionArc xlink:type="arc" order="77.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_EmployeeStockOwnershipPlanESOPSharesInESOP_1770" />
    <link:definitionArc xlink:type="arc" order="78.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedNumberOfShares_1771" />
    <link:definitionArc xlink:type="arc" order="79.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_1772" />
    <link:definitionArc xlink:type="arc" order="80.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_1773" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_EquityDetailsTable_1566" xlink:to="us-gaap_StatementEquityComponentsAxis_1582" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_CommonStockSharesIssued_1592" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare_1593" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_CommonStockSharesOutstanding_1594" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_CommonStockVotingRights_1595" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_1597" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_SaleOfStockPricePerShare_1598" />
    <link:definitionArc xlink:type="arc" order="25.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_DividendsPayableAmountPerShare_1607" />
    <link:definitionArc xlink:type="arc" order="26.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockLineItems_1591" xlink:to="us-gaap_DividendsPayableCurrent_1608" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementEquityComponentsAxis_1582" xlink:to="us-gaap_EquityComponentDomain_1583" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="glxg_EquityDetailsTable_1566" xlink:to="us-gaap_PlanNameAxis_1585" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_PlanNameAxis_1585" xlink:to="us-gaap_PlanNameDomain_1586" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_RangeAxis_1575" xlink:to="srt_RangeMember_1576_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_SubsidiarySaleOfStockAxis_1567" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain_1568_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementClassOfStockAxis_1570" xlink:to="us-gaap_ClassOfStockDomain_1571_default" />
    <link:definitionArc xlink:type="arc" order="107.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_CurrencyAxis_1809" xlink:to="currency_AllCurrenciesDomain_1810_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementEquityComponentsAxis_1582" xlink:to="us-gaap_EquityComponentDomain_1583_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_PlanNameAxis_1585" xlink:to="us-gaap_PlanNameDomain_1586_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/ConsolidatedStatementsofIncomeLossandComprehensiveIncomeLoss" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_EmploymentServicesMember" xlink:label="glxg_EmploymentServicesMember_1059" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_PayrollOutsourcingServicesMember" xlink:label="glxg_PayrollOutsourcingServicesMember_1060" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis" xlink:label="srt_ProductOrServiceAxis_1057" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_1080" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain" xlink:label="srt_ProductsAndServicesDomain_1058" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_1081" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_1082" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ResearchAndDevelopmentExpense" xlink:label="us-gaap_ResearchAndDevelopmentExpense_1067" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvisionForDoubtfulAccounts" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_1068" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpenses" xlink:label="us-gaap_OperatingExpenses_1069" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss" xlink:label="us-gaap_OperatingIncomeLoss_1070" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherIncomeAbstract" xlink:label="us-gaap_OtherIncomeAbstract_1071" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInterest" xlink:label="us-gaap_InvestmentIncomeInterest_1072" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseNonoperating" xlink:label="us-gaap_InterestExpenseNonoperating_1073" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems_1061" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenuesAbstract" xlink:label="us-gaap_RevenuesAbstract_1062" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues" xlink:label="us-gaap_Revenues_1063" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostOfRevenue" xlink:label="us-gaap_CostOfRevenue_1064" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_1083" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract" xlink:label="us-gaap_EarningsPerShareAbstract_1084" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic" xlink:label="us-gaap_EarningsPerShareBasic_1085" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted" xlink:label="us-gaap_EarningsPerShareDiluted_1086" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpensesAbstract" xlink:label="us-gaap_OperatingExpensesAbstract_1065" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SellingGeneralAndAdministrativeExpense" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_1066" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract" xlink:label="us-gaap_IncomeStatementAbstract_1055" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable_1056" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNonoperatingIncomeExpense" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_1074" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpense" xlink:label="us-gaap_NonoperatingIncomeExpense_1075" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_1076" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit_1077" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss_1078" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_1079" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain" xlink:label="srt_ProductsAndServicesDomain_1058_default" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ProductsAndServicesDomain_1058" xlink:to="glxg_EmploymentServicesMember_1059" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="srt_ProductsAndServicesDomain_1058" xlink:to="glxg_PayrollOutsourcingServicesMember_1060" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_StatementTable_1056" xlink:to="srt_ProductOrServiceAxis_1057" />
    <link:definitionArc xlink:type="arc" order="19.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_ComprehensiveIncomeNetOfTax_1080" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="srt_ProductOrServiceAxis_1057" xlink:to="srt_ProductsAndServicesDomain_1058" />
    <link:definitionArc xlink:type="arc" order="20.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_1081" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_1081" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_1082" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OperatingExpensesAbstract_1065" xlink:to="us-gaap_ResearchAndDevelopmentExpense_1067" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OperatingExpensesAbstract_1065" xlink:to="us-gaap_ProvisionForDoubtfulAccounts_1068" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OperatingExpensesAbstract_1065" xlink:to="us-gaap_OperatingExpenses_1069" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_OperatingIncomeLoss_1070" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_OtherIncomeAbstract_1071" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OtherIncomeAbstract_1071" xlink:to="us-gaap_InvestmentIncomeInterest_1072" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OtherIncomeAbstract_1071" xlink:to="us-gaap_InterestExpenseNonoperating_1073" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_RevenuesAbstract_1062" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_RevenuesAbstract_1062" xlink:to="us-gaap_Revenues_1063" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_CostOfRevenue_1064" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_1081" xlink:to="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_1083" />
    <link:definitionArc xlink:type="arc" order="21.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_EarningsPerShareAbstract_1084" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_EarningsPerShareAbstract_1084" xlink:to="us-gaap_EarningsPerShareBasic_1085" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_EarningsPerShareAbstract_1084" xlink:to="us-gaap_EarningsPerShareDiluted_1086" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_OperatingExpensesAbstract_1065" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OperatingExpensesAbstract_1065" xlink:to="us-gaap_SellingGeneralAndAdministrativeExpense_1066" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_StatementTable_1056" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OtherIncomeAbstract_1071" xlink:to="us-gaap_OtherNonoperatingIncomeExpense_1074" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_OtherIncomeAbstract_1071" xlink:to="us-gaap_NonoperatingIncomeExpense_1075" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_1076" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_IncomeTaxExpenseBenefit_1077" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_NetIncomeLoss_1078" />
    <link:definitionArc xlink:type="arc" order="18.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1061" xlink:to="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_1079" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="srt_ProductOrServiceAxis_1057" xlink:to="srt_ProductsAndServicesDomain_1058_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/ConsolidatedStatementsofIncomeLossandComprehensiveIncomeLossParentheticals" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember_1731" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember_1732" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract" xlink:label="us-gaap_IncomeStatementAbstract_1727" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable_1728" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis_1729" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1730" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems_1733" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_1734" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_34680" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityReverseStockSplit" xlink:label="us-gaap_StockholdersEquityReverseStockSplit_34681" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1730_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1730" xlink:to="us-gaap_CommonClassAMember_1731" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1730" xlink:to="us-gaap_CommonClassBMember_1732" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_StatementLineItems_1733" xlink:to="us-gaap_StatementTable_1728" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_StatementTable_1728" xlink:to="us-gaap_StatementClassOfStockAxis_1729" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementClassOfStockAxis_1729" xlink:to="us-gaap_ClassOfStockDomain_1730" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1733" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_1734" />
    <link:definitionArc xlink:type="arc" order="116.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1733" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare_34680" />
    <link:definitionArc xlink:type="arc" order="117.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1733" xlink:to="us-gaap_StockholdersEquityReverseStockSplit_34681" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementClassOfStockAxis_1729" xlink:to="us-gaap_ClassOfStockDomain_1730_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/ConsolidatedStatementsofChangesinShareholdersEquityParentheticals" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember_1741" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember_1742" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_1737" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable_1738" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis_1739" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityReverseStockSplit" xlink:label="us-gaap_StockholdersEquityReverseStockSplit_1812" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1740" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems_1743" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_1744" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_1745" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1740_default" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1740" xlink:to="us-gaap_CommonClassAMember_1741" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1740" xlink:to="us-gaap_CommonClassBMember_1742" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_StatementLineItems_1743" xlink:to="us-gaap_StatementTable_1738" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_StatementTable_1738" xlink:to="us-gaap_StatementClassOfStockAxis_1739" />
    <link:definitionArc xlink:type="arc" order="108.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1743" xlink:to="us-gaap_StockholdersEquityReverseStockSplit_1812" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementClassOfStockAxis_1739" xlink:to="us-gaap_ClassOfStockDomain_1740" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1743" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_1744" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1743" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare_1745" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementClassOfStockAxis_1739" xlink:to="us-gaap_ClassOfStockDomain_1740_default" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://galaxy-hk.com/20260630/role/ConsolidatedStatementsofChangesinShareholdersEquity" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember" xlink:label="us-gaap_AdditionalPaidInCapitalMember_1094" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember" xlink:label="us-gaap_RetainedEarningsMember_1095" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember" xlink:label="us-gaap_CommonStockMember_1091" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_SubscriptionReceivableMember" xlink:label="glxg_SubscriptionReceivableMember_1092" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_SharesReservedForIssuanceMember" xlink:label="glxg_SharesReservedForIssuanceMember_1093" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_1096" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember_1099" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember_1100" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis" xlink:label="us-gaap_StatementEquityComponentsAxis_1090" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesOutstanding" xlink:label="us-gaap_SharesOutstanding_1104" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_1105" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_1106" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueEmployeeStockOwnershipPlan" xlink:label="us-gaap_StockIssuedDuringPeriodValueEmployeeStockOwnershipPlan_1107" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesEmployeeStockOwnershipPlan" xlink:label="us-gaap_StockIssuedDuringPeriodSharesEmployeeStockOwnershipPlan_1108" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_StockIssuedDuringReclassificationAndRedesignationOfOrdinarySharesIntoClassAAndB" xlink:label="glxg_StockIssuedDuringReclassificationAndRedesignationOfOrdinarySharesIntoClassAAndB_1109" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain_1097" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis_1098" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1101" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems_1102" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity_1103" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_StockIssuedDuringPeriodSharesReclassificationAndRedesignationOfOrdinarySharesIntoClassAAndBinShares" xlink:label="glxg_StockIssuedDuringPeriodSharesReclassificationAndRedesignationOfOrdinarySharesIntoClassAAndBinShares_1110" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsCash" xlink:label="us-gaap_DividendsCash_1112" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss_1113" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax_1114" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueOther" xlink:label="us-gaap_StockIssuedDuringPeriodValueOther_1722" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesOther" xlink:label="us-gaap_StockIssuedDuringPeriodSharesOther_1723" />
    <link:loc xlink:type="locator" xlink:href="glxg-20260630.xsd#glxg_DistributionOfSharesUponESOP" xlink:label="glxg_DistributionOfSharesUponESOP_1724" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_1088" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable_1089" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain_1097_default" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1101_default" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_EquityComponentDomain_1097" xlink:to="us-gaap_AdditionalPaidInCapitalMember_1094" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_EquityComponentDomain_1097" xlink:to="us-gaap_RetainedEarningsMember_1095" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_EquityComponentDomain_1097" xlink:to="us-gaap_CommonStockMember_1091" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_EquityComponentDomain_1097" xlink:to="glxg_SubscriptionReceivableMember_1092" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_EquityComponentDomain_1097" xlink:to="glxg_SharesReservedForIssuanceMember_1093" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_EquityComponentDomain_1097" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeMember_1096" />
    <link:definitionArc xlink:type="arc" order="10.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1101" xlink:to="us-gaap_CommonClassAMember_1099" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_ClassOfStockDomain_1101" xlink:to="us-gaap_CommonClassBMember_1100" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_StatementTable_1089" xlink:to="us-gaap_StatementEquityComponentsAxis_1090" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_SharesOutstanding_1104" />
    <link:definitionArc xlink:type="arc" order="13.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues_1105" />
    <link:definitionArc xlink:type="arc" order="14.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_1106" />
    <link:definitionArc xlink:type="arc" order="15.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_StockIssuedDuringPeriodValueEmployeeStockOwnershipPlan_1107" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_StockIssuedDuringPeriodSharesEmployeeStockOwnershipPlan_1108" />
    <link:definitionArc xlink:type="arc" order="17.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="glxg_StockIssuedDuringReclassificationAndRedesignationOfOrdinarySharesIntoClassAAndB_1109" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementEquityComponentsAxis_1090" xlink:to="us-gaap_EquityComponentDomain_1097" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:from="us-gaap_StatementTable_1089" xlink:to="us-gaap_StatementClassOfStockAxis_1098" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:from="us-gaap_StatementClassOfStockAxis_1098" xlink:to="us-gaap_ClassOfStockDomain_1101" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_StockholdersEquity_1103" />
    <link:definitionArc xlink:type="arc" order="18.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="glxg_StockIssuedDuringPeriodSharesReclassificationAndRedesignationOfOrdinarySharesIntoClassAAndBinShares_1110" />
    <link:definitionArc xlink:type="arc" order="19.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_DividendsCash_1112" />
    <link:definitionArc xlink:type="arc" order="20.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_NetIncomeLoss_1113" />
    <link:definitionArc xlink:type="arc" order="21.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax_1114" />
    <link:definitionArc xlink:type="arc" order="22.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_StockIssuedDuringPeriodValueOther_1722" />
    <link:definitionArc xlink:type="arc" order="23.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_StockIssuedDuringPeriodSharesOther_1723" />
    <link:definitionArc xlink:type="arc" order="24.00000" priority="1" xbrldt:closed="false" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="glxg_DistributionOfSharesUponESOP_1724" />
    <link:definitionArc xlink:type="arc" order="11.00000" priority="1" xbrldt:closed="true" use="optional" xbrldt:contextElement="segment" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" xlink:from="us-gaap_StatementLineItems_1102" xlink:to="us-gaap_StatementTable_1089" />
    <link:definitionArc xlink:type="arc" order="16.00000" priority="1" xbrldt:closed="true" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementEquityComponentsAxis_1090" xlink:to="us-gaap_EquityComponentDomain_1097_default" />
    <link:definitionArc xlink:type="arc" order="12.00000" priority="1" xbrldt:closed="true" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:from="us-gaap_StatementClassOfStockAxis_1098" xlink:to="us-gaap_ClassOfStockDomain_1101_default" />
  </link:definitionLink>
  <link:roleRef roleURI="http://fasb.org/srt/role/srt-eedm/ExtensibleEnumerationLists" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-roles-2026.xsd#eedm1" xlink:type="simple" />
  <link:definitionLink xlink:role="http://fasb.org/srt/role/srt-eedm/ExtensibleEnumerationLists" xlink:type="extended" xlink:title="definitionLink">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TimingOfTransferOfGoodOrServiceDomain" xlink:label="us-gaap_TimingOfTransferOfGoodOrServiceDomain" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransferredOverTimeMember" xlink:label="us-gaap_TransferredOverTimeMember" />
    <link:definitionArc xlink:type="arc" order="0" priority="1" xbrldt:closed="true" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="us-gaap_TimingOfTransferOfGoodOrServiceDomain" xlink:to="us-gaap_TransferredOverTimeMember" />
  </link:definitionLink>
</link:linkbase>
