Exhibit 10.1

Execution Version

August 27, 2026

Mr. Richard P. Smith

At the address on file with TriCo

Dear Rick:

This letter (this “Letter Agreement”) memorializes our agreement regarding the terms of your employment with, and service to, First Hawaiian Bank (“FHB”) following the completion of the Merger contemplated by the Agreement and Plan of Reorganization and Merger, by and among First Hawaiian, Inc. (“FHI”), TriCo Bancshares (“TriCo”) and Horizon Merger Sub, Inc. (the “Merger Agreement”). Capitalized terms used but not defined in this Letter Agreement have the meanings ascribed to them in the Merger Agreement.

1.             Term

The term of this Letter Agreement shall commence on the Closing Date (such Closing Date, the “Effective Date”) and end on the third anniversary of the Effective Date (the “Term”). This Letter Agreement will be effective as of the Closing Date, provided that, if your employment with TriCo terminates for any reason before the Closing Date or if the Merger Agreement is terminated before the Closing Date in accordance with its terms, this Letter Agreement will automatically terminate and be void ab initio, and neither of the parties will have any obligations hereunder.

2.             Employment; Compensation

A.             Position; Reporting; Duties; Location

During the Term, you shall serve as a non-executive employee of FHB with the title of Chairman, Tri Counties Bank, and shall report directly and exclusively to the Chief Executive Officer of FHI and FHB (the “CEO”). During your tenure as Chairman, you shall have such duties and responsibilities as may from time to time be reasonably assigned to you by the CEO. Your services will be performed at the same location at which you provided services to TriCo prior to the Effective Date.

B.             Compensation

Annual Compensation. During the Term, your annual compensation (“Annual Compensation”) will be at the rate of $500,000, payable to you ratably in accordance with FHB’s generally applicable payroll practices. You shall also be paid any unpaid annual cash incentive award payable under the applicable TriCo short-term cash incentive program for the 2026 fiscal year (the “TriCo Annual Bonus”), payable at the same time as applies to other senior executives of TriCo generally.

Benefits; Perquisites. During the Term, you shall be entitled to participate in employee benefit plans, programs and arrangements on terms and conditions no less favorable than those provided to other senior executives of TriCo and will receive perquisites no less favorable than those provided to you immediately prior to Closing. Notwithstanding anything herein to the contrary, you will not be eligible to participate in any severance agreements, plans or arrangements for similarly situated employees of TriCo or FHB, and you will not be eligible for any cash bonus, incentive, or equity compensation (other than the Closing Date RSU Grant described in Section 3 below). The TriCo Bancshares Supplemental Executive Retirement Plan will remain in effect in accordance with its existing terms with respect to your participation therein as set out in your applicable Participation Agreement with TriCo.

3.             DC Amount; Closing Date RSU Grant; Good Reason Waiver

In full satisfaction of the obligations under Section 5(e) of your Employment Agreement with TriCo and Tri Counties Bank, dated as of April 12, 2021 (the “Existing Agreement”), no later than ten (10) business days following your execution (on or within twenty-one (21) days following the Effective Date) and non-revocation of a release of claims substantially in the form attached hereto as Exhibit A (the “Release”), FHB shall (A) pay you, in a single lump sum in cash, an amount equal to the sum of (1) an amount equal to two (2) times the lesser of (i) your annualized compensation, based on your Base Salary (as defined in the Existing Agreement) in effect immediately prior to the Effective Date, and (ii) the limit in effect under Section 401(a)(17) of the Internal Revenue Code of 1986, as amended (the “Code”), for the calendar year in which the Effective Date occurs, in each case determined in a manner consistent with Treasury Regulation Section 1.409A-1(b)(9)(iii)(A), plus (2) an additional amount equal to the aggregate amount that would have been paid to you under Section 5(e)(i)(1) and (2) of the Existing Agreement that qualifies as a “short-term deferral” within the meaning of Treasury Regulation Section 1.409A-1(b) (the sum of (1) and (2), “Closing Payment”), and (B) credit an amount an amount equal to the excess, if any, of (x) the aggregate amount that would have been payable to you under Section 5(e)(i)(1) and (2) of the Existing Agreement over (y) the Closing Payment (the “DC Amount”) to a deferred compensation account established in your name and bearing interest at the then-current prime rate. The DC Amount shall be fully vested and non-forfeitable at all times and shall be paid (plus earnings thereon) in equal installments on FHB’s regular payroll dates for a period of thirty-six (36) months following your “separation from service” within the meaning of Section 409A of the Internal Revenue Code of 1986, as amended, including the applicable regulations thereunder (“Section 409A”), subject to any required six-month delay under Section 409A if you are a “specified employee” for purposes of Section 409A on the date of separation from service and to your execution (upon or within twenty-one (21) days following such separation from service) and non-revocation of the Release.

In addition, on the Effective Date, FHI will grant you a one-time restricted stock unit award (the “Closing Date RSU Grant”) with a target grant value of $6,000,000, which will vest in equal quarterly installments over three (3) years from the Closing, with the last quarterly installment to occur on or immediately prior to the three (3)-year anniversary of the Closing, subject to your continued employment through each applicable vesting date (except as otherwise provided in this Agreement). The Closing Date RSU Grant is otherwise subject to the terms of the RSU grant agreement approved by the Compensation Committee of the Board of Directors of FHI (the “FHI Board”) as attached hereto as Exhibit B (the “RSU Agreement”) and the terms of the First Hawaiian, Inc. 2025 Omnibus Incentive Compensation Plan, as it may be amended from time to time.

In consideration of the foregoing, you hereby agree to waive any “Good Reason” or similar right under the Existing Agreement and any other agreement, arrangement or plan, including any equity incentive award, to which are subject with TriCo and any of its subsidiaries as a result of or in connection with (A) the Merger or (B) the changes to the terms of your employment as set out in this Letter Agreement.

4.             Early Termination

Your service as an employee under this Letter Agreement may not be terminated by FHB during the Term other than by FHB for Cause (as defined in the Existing Agreement, with references to “Employer” to refer to FHB as defined herein). Upon your termination of service hereunder for any reason, you will receive (A) the amount of the Annual Compensation that is earned but unpaid based on your provision of the services through the termination date, which will be paid in a lump sum within 30 days following the termination date (or such earlier date as may be required by applicable law), (B) the amount of any accrued but unused vacation pay, (C) any business expense reimbursements incurred by you as of the termination date and submitted for reimbursement, in each case, consistent with the policy for such reimbursements, within ten (10) days following the termination date, and (D) any other vested compensation or benefits to be paid as set forth in the applicable document governing such compensation or benefits (the amounts set forth in (A) through (D), collectively, the “Accrued Amounts”). Except as set forth below or as otherwise provided in the Merger Agreement, neither FHI nor FHB shall have any further obligations to you beyond the Accrued Amounts. For the avoidance of doubt, cessation of service on the FHI Board or the Board of Directors of FHB (the “FHB Board”, together with the FHI Board, the “Boards”) (as described in Section 5, below) will not constitute a termination of your service as an employee under this Letter Agreement or, provided that FHI and FHB, as applicable, have satisfied their obligations below under Section 5 of this Letter Agreement, be considered a material breach hereof by either party.

If, prior to the expiration of the Term, your service hereunder is terminated due to your death, then, in addition to the Accrued Amounts, the remainder of the Annual Compensation that you would have received had you remained employed by FHB for the duration of the Term will continue to be paid to your estate or legal representative, as applicable, in accordance with Section 2(B) of this Letter Agreement.

You hereby acknowledge that if your service as an employee is terminated for any reason, the restrictive covenants set forth in Section 8 of the Existing Agreement and your obligation to comply with such restrictive covenants (the “Existing Restrictive Covenants”) will remain in full force and effect, and the Existing Restrictive Covenants are hereby incorporated herein by reference.

For the avoidance of doubt, your separate indemnification agreements with each of TriCo and Tri Counties Banks (as described in Section 10(c) of the Existing Agreement) (the “Indemnification Agreements”) shall survive the execution of this Letter Agreement and remain in full force and effect as if fully set forth herein, and TriCo and FHB shall continue to honor all of their obligations thereunder, which expressly survive any termination of this Agreement.

5.             Board Service

Commencing on the Effective Date, you shall be appointed to serve as a member of the Boards. Thereafter for the duration of the Term, subject to your continued compliance with FHI’s and FHB’s policies applicable to members of the Boards, FHI and FHB, as applicable, shall nominate you annually to serve on the Boards consistent with their respective practices for nominating other members of the Boards.

For the avoidance of doubt, the Compensation set forth in Section 2(B), together with the Closing Date RSU Grant described above, will constitute your sole compensation for your service under this Letter Agreement; you will not be entitled to receive any compensation in respect of your service as a member of the Boards.

6.             Section 409A; Section 280G

It is the intent of the parties that the payments and benefits under this Letter Agreement will be exempt from or otherwise comply with the provisions of Section 409A, and this Letter Agreement will be administered and interpreted in a manner consistent with this intent. Any payments that qualify for the “short-term deferral” exception, the separation pay exception or another exception under Section 409A shall be paid under the applicable exception. Each payment and benefit under this Letter Agreement will be treated as a separate payment for purposes of Section 409A. In no event may you, directly or indirectly, designate the calendar year of payment. The parties intend that the terms and provisions of this Letter Agreement will be interpreted and applied in a manner that satisfies the requirements and exemptions of Section 409A. All reimbursements of costs and expenses or in-kind benefits provided under this Letter Agreement will be made or provided in accordance with Section 409A, including, where applicable, that the right to reimbursement or in-kind benefits will not be subject to liquidation and may not be exchanged for any other benefit, the amount of expenses eligible for reimbursement (or in-kind benefits paid) in one year will not affect amounts reimbursable or provided as in-kind benefits in any subsequent year, and all expense reimbursements that are taxable income to you will in no event be paid later than the end of the calendar year next following the year in which you incur the expense.

Notwithstanding any other provision of this Letter Agreement to the contrary, if you are considered a “specified employee” for purposes of Section 409A (as determined in accordance with the methodology established by FHI or FHB, as applicable, as in effect on the date of termination), any payment that constitutes nonqualified deferred compensation within the meaning of Section 409A that is otherwise due to you under this Letter Agreement during the six (6)-month period following your separation from service (as determined in accordance with Section 409A) on account of your separation from service will be accumulated and paid to you on the first business day of the seventh (7^th) month following your separation from service (the “Delayed Payment Date”). If you die during the postponement period, the amounts and entitlements delayed on account of Section 409A will be paid to the personal representative of your estate on the first to occur of the Delayed Payment Date or thirty (30) calendar days after the date of your death.

Section 5(h) of the Existing Agreement (IRC Section 280G) is hereby incorporated herein by reference.

7.             Existing Rights; Entire Agreement

Upon the Effective Date, the Existing Agreement will terminate and be of no force or effect, except that Section 8 of the Existing Agreement (Business Protection Covenants), including the Existing Restrictive Covenants set forth therein, Section 5(h) of the Existing Agreement (IRC Section 280G) and the Indemnification Agreements shall survive the effectiveness of this Letter Agreement and remain in full force and effect as if fully set forth herein, and TriCo and FHB shall continue to honor all of their obligations thereunder.

8.             Miscellaneous

This Letter Agreement is personal to you and, without the prior written consent of FHB, shall not be assignable by you. This Letter Agreement and any rights and benefits hereunder will inure to the benefit of and be enforceable by your legal representatives, heirs, or legatees. This Letter Agreement and any rights and benefits hereunder will inure to the benefit of and be binding upon FHB and its successors and assigns.

This Letter Agreement will be governed and construed in accordance with the laws of the State of California, without regard to conflict of laws principles thereof. This Letter Agreement may not be amended or modified other than by a written agreement executed by the parties hereto or their respective successors and legal representatives.

The invalidity or unenforceability of any provision of this Letter Agreement will not affect the validity or enforceability of any other provision of this Letter Agreement, and this Letter Agreement will be construed as if such invalid or unenforceable provision were omitted (but only to the extent that such provision cannot be appropriately re-formed or modified).

FHI and FHB may withhold from any amounts payable under this Letter Agreement such federal, state, local, or foreign taxes as shall be required to be withheld pursuant to any applicable law or regulation.

FHB’s obligation to make the payments provided for in this Letter Agreement and otherwise to perform its obligations hereunder will not (absent your material violation of the Existing Restrictive Covenants) be affected by any set-off, counterclaim, defense, or other claim, right, or action that FHB or its subsidiaries or affiliates may have against you or others.

Upon the expiration or termination of this Letter Agreement or your services, the respective rights and obligations of the parties hereto, including your obligations under the Existing Restrictive Covenants, shall survive such expiration or termination consistent with the terms of this Letter Agreement and otherwise to the extent necessary to carry out the intentions of the parties hereunder.

Any notices given under this Letter Agreement (1) by FHB to you will be in writing and will be given by hand delivery or by registered or certified mail, return receipt requested, postage prepaid, addressed to you at your address listed above, with a copy (which shall not constitute notice) to Jeremy L. Goldstein, Sterlington PLLC (jeremy.goldstein@sterlingtonlaw.com; notices@sterlingtonlaw.com) or (2) by you to FHB will be in writing and will be given by hand delivery or by registered or certified mail, return receipt requested, postage prepaid, addressed to the General Counsel of FHB at FHB’s corporate headquarters.

This Letter Agreement sets forth the entire agreement of the parties hereto in respect of the subject matter contained herein and, except as provided herein, supersedes any other agreement or understanding between the parties with respect to the subject matter hereof. The headings of this Letter Agreement are for reference purposes only and will not affect in any way the meaning or interpretation of this Letter Agreement.

This Letter Agreement may be executed in separate counterparts, each of which will be deemed to be an original but all of which taken together constitute one and the same agreement. Delivery of an executed counterpart of a signature page to this Letter Agreement by electronic transmission, including in portable document format (.pdf), shall be deemed as effective as delivery of an original executed counterpart of this Letter Agreement.

[Signature Page Follows]

If this Letter Agreement correctly describes our understanding, please execute and deliver a counterpart of this signature page, which will become a binding agreement upon our receipt.

Accepted and Agreed

I hereby agree with and accept the terms
and conditions of this Letter Agreement:

[Signature Page to Letter Agreement]