Exhibit (e)

BLACKROCK 2037 MUNICIPAL TARGET TERM TRUST

AUTOMATIC DIVIDEND REINVESTMENT PLAN

TERMS AND CONDITIONS

Pursuant to this Automatic Dividend Reinvestment Plan (the “Reinvestment Plan”) of the undersigned BlackRock 2037 Municipal Target Term Trust (the “Fund”), unless a holder (a “Shareholder”) of the Fund’s common shares of beneficial interest (the “Common Shares”) otherwise elects, all dividends and distributions (together, “distributions”) on such Shareholder’s Common Shares will be automatically reinvested by Computershare Trust Company, N.A. (“Computershare”), as agent for Shareholders in administering the Reinvestment Plan (the “Reinvestment Plan Agent”), in additional Common Shares of the Fund. Shareholders who elect not to participate in the Reinvestment Plan will receive all dividends and other distributions in cash paid by check mailed directly to the Shareholder of record (or, if the Common Shares are held in street or other nominee name, then to such nominee) by Computershare as the Dividend Disbursing Agent. Participants may elect not to participate in the Reinvestment Plan and to receive all dividends and distributions in cash by sending written instructions to Computershare, as the Dividend Disbursing Agent, at the address set forth below. Participation in the Reinvestment Plan is completely voluntary and may be terminated or resumed at any time without penalty by written notice if received and processed by the Reinvestment Plan Agent prior to the dividend or distribution record date; otherwise such termination or resumption will be effective with respect to any subsequently declared dividend or distribution.

The Reinvestment Plan Agent will open an account for each Shareholder under the Reinvestment Plan in the same name in which such Shareholder’s Common Shares are registered. Whenever the Fund declares a dividend or a distribution (collectively referred to as “dividends”) payable in cash, non-participants in the Reinvestment Plan will receive cash and participants in the Reinvestment Plan will receive the equivalent in Common Shares. The Common Shares will be acquired by the Reinvestment Plan Agent for the participants’ accounts by purchasing outstanding Common Shares on the open market (“open-market purchases”) on the New York Stock Exchange, the primary national securities exchange on which the Common Shares are traded, or elsewhere. The Fund will not issue any new Common Shares under this Reinvestment Plan. The Reinvestment Plan Agent will have until the last business day before the next date on which the Common Shares trade on an “ex-dividend” basis or 30 days after the payment date for such dividend, whichever is sooner (the “last purchase date”), to invest the dividend amount in Common Shares acquired in open-market purchases. It is contemplated that the Fund will pay monthly dividends.

The Reinvestment Plan Agent will maintain all Shareholders’ accounts in the Reinvestment Plan and furnish written confirmation of all transactions in the accounts, including information needed by Shareholders for tax records. Common Shares in the account of each Reinvestment Plan participant will be held by the Reinvestment Plan Agent on behalf of the Reinvestment Plan participant.

In the case of Shareholders such as banks, brokers or nominees that hold Common Shares for others who are the beneficial owners, the Reinvestment Plan Agent will administer the Reinvestment Plan on the basis of the number of Common Shares certified from time to time by the record Shareholder and held for the account of beneficial owners who participate in the Reinvestment Plan.

The Reinvestment Plan Agent’s fees for the handling of the reinvestment of dividends will be paid by the Fund. However, each participant will pay a per share fee incurred with respect to the Reinvestment Plan Agent’s open-market purchases in connection with the reinvestment of dividends, which will be deducted from the value of the dividends. Participants that request a sale of Common Shares through the Reinvestment Plan Agent are subject to a $2.50 sales fee and a brokerage commission of $0.15 per Common Share sold.

VOTING

Each Shareholder proxy will include those Common Shares purchased or received pursuant to the Reinvestment Plan. The Reinvestment Plan Agent will forward all proxy solicitation materials to participants and vote proxies for Common Shares held pursuant to the Reinvestment Plan in accordance with the instructions of the participants.

TAXATION

The automatic reinvestment of dividends will not relieve participants of any U.S. federal, state or local income tax that may be payable (or required to be withheld) on such dividends.

AMENDMENT OF THE REINVESTMENT PLAN

The Reinvestment Plan may be amended or terminated by the Fund. There is no direct service charge to participants with regard to purchases in the Reinvestment Plan; however, the Fund reserves the right to amend the Reinvestment Plan to include a service charge payable by the participants. Notice will be sent to Reinvestment Plan participants of any amendments as soon as practicable after such action by the Fund.

INQUIRIES REGARDING THE REINVESTMENT PLAN

All correspondence concerning the Reinvestment Plan should be directed to the Reinvestment Plan Agent, through the internet at www.computershare.com/blackrock, or in writing to Computershare, P. O. Box 505000, Louisville, KY 40233, Telephone: (800) 699-1236. Overnight correspondence should be directed to the Reinvestment Plan Agent at Computershare, 462 South 4th Street, Suite 1600, Louisville, KY 40202.

APPLICABLE LAW

These terms and conditions shall be governed by the laws of the State of New York without regard to its conflicts of laws provisions.

EXECUTION

To record the adoption of the Reinvestment Plan as of                             , 2022, the Fund has caused this Reinvestment Plan to be executed in the name and on behalf of the Fund by a duly authorized officer.

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Signature Page to Dividend Reinvestment Plan