<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019e1d0b-68b3-7296-9cc1-d66567a1f463,g:c01789c8-b382-493b-adb9-dca7994a0ead-->
<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" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://cbtcares.com/role/Cover" xlink:type="simple" xlink:href="care-20260723.xsd#Cover"/>
  <link:presentationLink xlink:role="http://cbtcares.com/role/Cover" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType_019e1d0b-68b3-77ee-a2f3-9832ab8c6f47" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_DocumentType_019e1d0b-68b3-77ee-a2f3-9832ab8c6f47" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate_019e1d0b-68b3-7368-8fa3-4ba1a9f8416e" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentPeriodEndDate"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_DocumentPeriodEndDate_019e1d0b-68b3-7368-8fa3-4ba1a9f8416e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName_019e1d0b-68b3-7243-ab95-6f41001ee0f7" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_EntityRegistrantName_019e1d0b-68b3-7243-ab95-6f41001ee0f7" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode_019e1d0b-68b3-7294-9b0f-49679f7f0af1" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_EntityIncorporationStateCountryCode_019e1d0b-68b3-7294-9b0f-49679f7f0af1" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber_019e1d0b-68b3-7863-9835-dd0428524e68" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFileNumber"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_EntityFileNumber_019e1d0b-68b3-7863-9835-dd0428524e68" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber_019e1d0b-68b3-796b-8687-f3fa33e0d475" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_EntityTaxIdentificationNumber_019e1d0b-68b3-796b-8687-f3fa33e0d475" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1_019e1d0b-68b3-7ada-af3d-dacf053b8386" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine1"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_EntityAddressAddressLine1_019e1d0b-68b3-7ada-af3d-dacf053b8386" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown_019e1d0b-68b3-7853-9a7f-81a2447b0b30" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_EntityAddressCityOrTown_019e1d0b-68b3-7853-9a7f-81a2447b0b30" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince_019e1d0b-68b3-7333-a47c-683498959072" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_EntityAddressStateOrProvince_019e1d0b-68b3-7333-a47c-683498959072" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode_019e1d0b-68b3-7092-89ac-692f6a100c26" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_EntityAddressPostalZipCode_019e1d0b-68b3-7092-89ac-692f6a100c26" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode_019e1d0b-68b3-7df0-bbb6-64c3107365b2" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_CityAreaCode_019e1d0b-68b3-7df0-bbb6-64c3107365b2" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber_019e1d0b-68b3-70bb-b0e4-b3812e34c70c" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_LocalPhoneNumber_019e1d0b-68b3-70bb-b0e4-b3812e34c70c" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_WrittenCommunications_019e1d0b-68b3-7360-af30-2ec332abba56" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_WrittenCommunications"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_WrittenCommunications_019e1d0b-68b3-7360-af30-2ec332abba56" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SolicitingMaterial_019e1d0b-68b3-752b-b06b-39819f4bd052" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SolicitingMaterial"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_SolicitingMaterial_019e1d0b-68b3-752b-b06b-39819f4bd052" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementTenderOffer_019e1d0b-68b3-7c48-b1ca-f6382d18e2b3" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_PreCommencementTenderOffer"/>
    <link:presentationArc order="15" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_PreCommencementTenderOffer_019e1d0b-68b3-7c48-b1ca-f6382d18e2b3" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_PreCommencementIssuerTenderOffer_019e1d0b-68b3-78e4-9540-e12585530f8f" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <link:presentationArc order="16" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_PreCommencementIssuerTenderOffer_019e1d0b-68b3-78e4-9540-e12585530f8f" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle_019e1d0b-68b3-7747-a017-e08f08d99afa" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:presentationArc order="17" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_Security12bTitle_019e1d0b-68b3-7747-a017-e08f08d99afa" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol_019e1d0b-68b3-77a9-be48-f0ac684c86d9" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
    <link:presentationArc order="18" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_TradingSymbol_019e1d0b-68b3-77a9-be48-f0ac684c86d9" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName_019e1d0b-68b3-7cfa-be6b-2e23ac3cd34e" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName"/>
    <link:presentationArc order="19" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_SecurityExchangeName_019e1d0b-68b3-7cfa-be6b-2e23ac3cd34e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany_019e1d0b-68b3-7bae-986a-ac7539af73bb" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:presentationArc order="20" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_EntityEmergingGrowthCompany_019e1d0b-68b3-7bae-986a-ac7539af73bb" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey_019e1d0b-68b3-736f-bd59-938cfc0115da" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:presentationArc order="21" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_EntityCentralIndexKey_019e1d0b-68b3-736f-bd59-938cfc0115da" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus_019e1d0b-68b3-7f78-85cc-b19d7713a27e" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:presentationArc order="22" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_DocumentFiscalPeriodFocus_019e1d0b-68b3-7f78-85cc-b19d7713a27e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus_019e1d0b-68b3-75a2-9b09-244d1e0b781e" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalYearFocus"/>
    <link:presentationArc order="23" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_DocumentFiscalYearFocus_019e1d0b-68b3-75a2-9b09-244d1e0b781e" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag_019e1d0b-68b3-7e80-b637-b74051b93fcb" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag"/>
    <link:presentationArc order="24" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_dei_CoverAbstract_019e1d0b-68b3-7003-9540-5d71daa3fd55" xlink:to="loc_dei_AmendmentFlag_019e1d0b-68b3-7e80-b637-b74051b93fcb" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
  </link:presentationLink>
</link:linkbase>
