THE FIRST TRUST COMBINED SERIES 629 TRUST AGREEMENT Dated: February 15, 2024

THE FIRST TRUST COMBINED SERIES 629

TRUST AGREEMENT

Dated: February 15, 2024

This Trust Agreement among First Trust Portfolios L.P., as Depositor, The Bank of New York Mellon, as Trustee and First Trust Advisors L.P., as Portfolio Supervisor sets forth certain provisions in full and incorporates other provisions by reference to the document entitled "Standard Terms and Conditions of Trust for The First Trust Combined Series 616 and subsequently deposited Series, effective October 27, 2022" (herein called the "Standard Terms and Conditions of Trust"), and such provisions as are set forth in full and such provisions as are incorporated by reference constitute a single instrument. All references herein to Articles and Sections are to Articles and Sections of the Standard Terms and Conditions of Trust.

WITNESSETH THAT:

In consideration of the premises and of the mutual agreements herein contained, the Depositor, the Trustee, the Portfolio Supervisor agree as follows:

PART I

STANDARD TERMS AND CONDITIONS OF TRUST

Subject to the Provisions of Part II and Part III hereof, all the provisions contained in the Standard Terms and Conditions of Trust are herein incorporated by reference in their entirety and shall be deemed to be a part of this instrument as fully and to the same extent as though said provisions had been set forth in full in this instrument. Facsimile or electronic signatures (including signatures in Portable Document Format (PDF)) to this Trust Agreement shall be acceptable and binding, and this Trust Agreement may be delivered by facsimile or other electronic means (including by electronic mail or a designated document storage website) confirmed by electronic mail.

PART II

SPECIAL TERMS AND CONDITIONS OF TRUST

TAX EXEMPT MUNICIPAL INCOME TRUST, SERIES 333

The following special terms and conditions are hereby agreed to:

A.The Securities defined in Section 1.01(22) listed in Schedule A hereto have been deposited in trust under this Trust Agreement.

B.The fractional undivided interest in and ownership of the Trust Fund represented by each Unit for a Trust on the Initial Date of Deposit is the amount set forth under the caption "Fractional Undivided Interest in the Trust per Unit" in the section entitled "Summary of Essential Information" in the Prospectus.

C.The number of units in a Trust on the Initial Date of Deposit referred to in Section 2.03 is set forth under the caption "Initial Number of Units" in the section entitled "Summary of Essential Information" in the Prospectus.

D.The approximate amount, if any, which the Trustee shall be required to advance out of its own funds and cause to be paid to the Depositor pursuant to the second sentence of Section 3.05 shall be the amount per Unit for each Trust that the Trustee agreed to reduce its fee or pay Trust Fund expenses set forth in the footnotes to the "Fee Table" for each Trust in the Prospectus times the number of units for such Trust referred to in Part II C. of this Trust Agreement.

E.For each Trust the First General Record Date and the amount of the second distribution of funds from the Interest Account shall be the record date for the Interest Account and the amount set forth under "Summary of Essential Information" in the Prospectus.

F.For each Trust the "First Settlement Date" is the date set forth under "Summary of Essential Information-First Settlement Date" for such Trust in the Prospectus.

G.First Trust Advisors L.P.'s compensation as referred to in Section 3.15 of the Standard Terms and Conditions of Trust and First Trust Portfolios L.P.’s compensation as referred to in Section 4.03 of the Standard Terms and Conditions of Trust shall be an annual aggregate fee in the amount of $.81 per Unit. The Trustee shall pay such aggregate amount to First Trust Advisors L.P. which shall be responsible to remit the Depositor’s fee to First Trust Portfolios L.P. First Trust Advisors L.P. shall confirm such remittance and the amount thereof to the Trustee upon request.

H.The Trustee's compensation as referred to in Section 6.04 of the Standard Terms and Conditions of Trust shall be an annual fee in the amount of $1.28 per Unit, calculated based on the largest number of Units outstanding during the calendar year except during the initial offering period as determined in Section 4.01 of this Indenture, in which case the fee is calculated based on the largest number of Units outstanding during the period for which the compensation is paid (such annual fee to be pro rated for any calendar year in which the Trustee provides service during less than the whole of such year). However, in no event, except as may otherwise be provided in the Standard Terms and Conditions of Trust, shall the Trustee receive compensation in any one year from any Trust of less than $2,000 for such annual compensation.

X.Xx Unit holder will be eligible for an in-kind distribution of Securities pursuant to Section 5.02.

X.Xx Unit holder will be eligible for an in-kind distribution of Securities pursuant to Section 8.02.

PART III

IN WITNESS WHEREOF, First Trust Portfolios L.P., The Bank of New York Mellon and First Trust Advisors L.P. have each caused this Trust Agreement to be executed and the respective corporate seal to be hereto affixed and attested (if applicable) by authorized officers; all as of the day, month and year first above written.

FIRST TRUST PORTFOLIOS L.P.,

 Depositor

First Trust Advisors L.P.,

 Portfolio Supervisor

By /s/ Xxxxxxxxx X. Xxxx
 Senior Vice President of:

  First Trust Portfolios L.P. and

  First Trust Advisors L.P.

THE BANK OF NEW YORK MELLON, Trustee

By /s/ Xxx X. Xxx

Vice President

SCHEDULE A TO TRUST AGREEMENT

SECURITIES INITIALLY DEPOSITED

IN

THE FIRST TRUST COMBINED SERIES 629

(Note: Incorporated herein and made a part hereof is the "Portfolio" as set forth for each Trust in the Prospectus.)