Exhibit (d)(3)

+ Computershare Trust Company, N.A. 150 Royall Street Suite V Canton Massachusetts 02021 Information Agent: Georgeson LLC Banks, Brokers and Shareholders call toll-free: (888) 206-5970 MR A SAMPLE DESIGNATION (IF ANY) ADD 1 ADD 2 ADD 3 NNNNNN ADD 4 ADD 5 NNNNNNNNN ADD 6 C 1234567890 J N T NNNNNN Primary Subscription 12345678901234 Rights SUBSCRIPTION RIGHTS CERTIFICATE VOID IF NOT RECEIVED BY THE SUBSCRIPTION AGENT BEFORE 5:00 PM EASTERN TIME ON JUNE 18, 2025 (UNLESS EXTENDED) (THE “EXPIRATION DATE”) BLACKROCK CORE BOND TRUST SUBSCRIPTION RIGHTS FOR COMMON SHARES (Complete appropriate section on reverse side of this form The registered holder (the “Holder”) of this Subscription Certificate named below, or the assignee, is entitled to the number of transferable Rights shown above to subscribe for common shares of beneficial interest, $0.001 par value per share (the “Common Shares”), of BlackRock Core Bond Trust (the “Fund”), in the ratio of one Common Share for each three Rights, pursuant to the primary subscription (the “Primary Subscription”) and upon the terms and conditions and at the price for each Common Share specified in the Prospectus Supplement, dated May 27, 2025, and the accompanying Prospectus, dated May 15, 2025, as supplemented to date (collectively the “Prospectus”) relating thereto. If you are a Record Date Common Shareholder and were issued fewer than three Rights, you are entitled to subscribe for one Common Share. To subscribe for Common Shares the Holder must present to Computershare Trust Company, N.A. (the “Subscription Agent” or “Computershare”), prior to 5:00 p.m., Eastern time, on the Expiration Date of June 18, 2025 (unless extended), either: (a) a properly completed and executed Subscription Certificate and a check drawn on a bank located in the United States and payable to “Computershare” for an amount equal to the number of Common Shares subscribed for under the Primary Subscription (and, if such Holder is a Record Date Common Shareholder electing to exercise the Over-Subscription Privilege, pursuant to the terms of the Over-Subscription Privilege) multiplied by the estimated Subscription Price; or (b) a notice of guaranteed delivery (the “Notice of Guaranteed Delivery”) guaranteeing delivery of a properly completed and executed Subscription Certificate. Under the Over-Subscription Privilege, as described in the Prospectus, any number of additional Common Shares may be purchased by a Record Date Common Shareholder if such Common Shares are available and the owner’s Rights under the Primary Subscription have been fully exercised and the pro rata allocation requirements have been satisfied. Any additional payment required from a participating Holder of Rights must be received by the Subscription Agent by 5:00 p.m., Eastern time, on the Expiration Date of June 18, 2025 unless the Offer is extended. Any excess payment to be refunded by the Fund to a Record Date Common Shareholder who is not allocated the full amount of Common Shares subscribed for pursuant to the Over-Subscription Privilege will be returned to him or her by mail by the Subscription Agent as promptly as practicable. A participating Holder of Rights will have no right to rescind a purchase after the Subscription Agent has received a properly completed and executed Subscription Certificate and payment by means of a check. This Subscription Certificate may be transferred, in the same manner and with the same effect as in the case of a negotiable instrument payable to specific persons, by duly completing and signing the assignment on the reverse side hereof. Capitalized terms used but not defined in this Subscription Certificate shall have the meanings assigned to them in the Prospectus relating to the Rights. This Subscription Certificate shall be governed by and construed in accordance with the laws of the State of Delaware. To subscribe pursuant to the Primary Subscription, three Rights and the estimated Subscription Price, which is [____], are required for each Common Share, and to subscribe pursuant to the Over-Subscription Privilege, the estimated Subscription Price is required for each Common Share. Payment of [____] per Common Share must accompany the Subscription Certificate. See the reverse side for forms. Holder ID COY Class Rights Qty Issued Rights Cert # 123456789 XXXX Subscription Rights XXX.XXXXXX 12345678 Signature of Owner and U.S. Person for Tax Certification Signature of Co-Owner (if more than one registered holder listed) Date (mm/dd/yyyy)

. PLEASE FILL IN ALL APPLICABLE INFORMATION. A (3. Rights Primary =1 Subscription Common Share) ___________________________ (Rights Exercised) ÷ 3 = ___________________________ (No. of Common Shares) x (Estimated Subscription $0.00 Price) = $____________________ B . Over-Subscription Privilege* ___________________________ (No. of Common Shares) x (Estimated Subscription $0.00 Price) = $____________________ * The Over-Subscription Privilege may only be exercised if the Primary Subscription Right is exercised to the fullest extent possible and may only be exercised by Record Date Shareholders as described in the Prospectus. Over-subscriptions may not be accepted by the Fund and are subject to pro rata reductions. C. Amount of Check Enclosed (A + B) (or amount in Notice of Guaranteed Delivery) = $___________________ D. The following broker-dealer is being designated as having been instrumental in the exercise of this Subscription Right: _______________________________ E. ☐ Sell any remaining unexercised Rights (submit to Agent by June 11, 2025) ☐ Sell all of my Rights (submit to Agent by June 11, 2025) SECTION 1. TO SUBSCRIBE: I acknowledge that I have received the Prospectus for the Rights Offering and I hereby irrevocably subscribe for the number of Common Shares indicated as the total of A and B hereon upon the terms and conditions specified in the Prospectus. I hereby agree that if I fail to pay for the Common Shares for which I have subscribed (or are deemed to have subscribed for as set forth above), the Fund may exercise any of the remedies set forth in the Prospectus. TO SELL: If I have checked the box on line E, I authorize the sale of Rights by the Subscription Agent according to the procedures described in the Prospectus. Signature(s) of Subscriber(s)/Seller(s) ______________________________________________________________________________________________________________________ Please give your telephone number: ( ) ___________________________________________________________________________________________________________________ Please give your e-mail address: __________________________________________________________________________________________________________________________ SECTION 2. TO TRANSFER RIGHTS: For value received, _____of the Rights represented by this Subscription Certificate are assigned to: (Print Full Name of Assignee) _____________________________________________________________________________________________________________________________ Social Security Number (Print Full Address) _____________________________________________________________________________________________________________________________________ (Print Full Address) _____________________________________________________________________________________________________________________________________ Signature(s) of Assignor(s) _______________________________________________________________________________________________________________________________ IMPORTANT: The signature(s) must correspond in every particular, without alteration, with the name(s) as printed on your Subscription Certificate. Your Signature must be guaranteed by an Eligible Guarantor Institution as that term is defined under Rule 17Ad-15 of the Securities Exchange Act of 1934, which may include: a) a commercial bank or trust company, or b) a member firm of a domestic stock exchange, or c) a savings bank or credit union. Signature Guaranteed By: _____________________________________ _____________________________________ (Name of Bank or Firm) (Signature of Officer and Title) Return Subscription Certificate by first class mail or overnight courier to: Computershare. By First Class Mail: By Express Mail or Overnight Courier: Computershare Computershare C/O Voluntary Corporate Actions C/O Voluntary Corporate Actions P.O. Box 43011 150 Royall Street Suite V Providence, RI 02940-3011 Canton, MA 02021