Exhibit (d)(4)

GREAT ELM CAPITAL CORP.

FORM OF NOTICE TO STOCKHOLDERS WHO ARE ACTING AS NOMINEES

Up to 10,761,950 Shares of Common Stock Issuable Upon Exercise of Non-Transferable Rights

[        ], 2020

Dear Stockholder:

Enclosed for your consideration is a prospectus, dated [        ], 2020 (the “Prospectus”), relating to the offering by Great Elm Capital Corp., a Maryland corporation (the “Company”), of non-transferable subscription rights (the “Rights”) to subscribe for up to an aggregate of 10,761,950 shares of the Company’s common stock, par value $0.01 per share (the “Common Stock”). The Rights will be issued to stockholders of record (the “Record Date Stockholders”) as of 5:00 p.m., New York City time, on September 4, 2020 (the “Record Date”). The Rights are offered on the terms and subject to the conditions described in the Prospectus.

The Rights may be exercised at any time during the subscription period, which commences on September 8, 2020 and ends at 5:00 p.m., New York City time, on September 28, 2020, unless extended by the Company in its sole discretion (the “Expiration Date”). The Rights are non-transferable and will not be listed for trading on the Nasdaq Global Market. The Rights may not be purchased or sold, and there will not be any market for trading the Rights. The shares of the Common Stock to be issued pursuant to the offering will be listed for trading on the Nasdaq Global Market under the symbol “GECC”.

The Rights will expire and be of no value if not exercised on or prior to the Expiration Date.

As described in the Prospectus, each Record Date Stockholder is entitled to receive one Right for each outstanding share of Common Stock owned on the Record Date. The Rights entitle the Record Date Stockholders to purchase one new share of Common Stock for every one Right held (the “primary subscription right”) at the subscription price (the “Subscription Price”), to be calculated as described in the Prospectus as of the Expiration Date. Record Date Stockholders who fully exercise their primary subscription right will be entitled to subscribe, subject to the limitations described in the Prospectus and subject to allotment, for additional shares of Common Stock that were not subscribed for by the Record Date Stockholders (the “over-subscription privilege”).

The Subscription Price per share will be 85% of the volume-weighted average of the market prices of the Company’s shares of Common Stock on the Nasdaq Global Market for the five consecutive trading days ending on the Expiration Date. As a result, the Company is requiring that Rights holders who wish to exercise their Rights deliver to American Stock Transfer & Trust Company, LLC, the subscription agent for the offering (the “Subscription Agent”) the estimated subscription price of $4.52 per share (the “Estimated Subscription Price”) on or before the Expiration Date as indicated in the Section entitled “The Offering—Payment for Shares” in the Prospectus. In the event that the Subscription Price exceeds the Estimated Subscription Price, an invoice will be sent for any additional amounts due. Payment for such additional amounts, if any, must be made within ten business days after the confirmation date. In the event the Subscription Price is less than the Estimated Subscription Price, the Subscription Agent will mail a refund to exercising Rights holders. No interest or penalty will be paid on amounts refunded.

The Rights will be evidenced by subscription rights certificates (the “Subscription Rights Certificates”) registered in your name or the name of your nominee. Each beneficial owner of shares of Common Stock registered in your name or the name of your nominee is entitled to one Right for each share of Common Stock owned by such beneficial owner as of the Record Date. No fractional shares of Common Stock will be issued pursuant to the Rights.

You will be required to submit payment in full for all of the shares of Common Stock you wish to purchase pursuant to the exercise of the Rights on or prior to the Expiration Date. Rights holders who exercise their Rights will have no right to rescind their subscription after receipt of their completed Subscription Rights Certificates together with payment for shares by the subscription agent.

We are asking persons who hold shares of Common Stock beneficially, and who have received the Rights distributable with respect to those shares through a broker-dealer, trust company, bank or other nominee, to contact the appropriate institution or nominee and request it to effect the transactions for them.

If you exercise the over-subscription privilege on behalf of beneficial owners of Rights, you will be required to certify to the Subscription Agent and the Company, in connection with the exercise of the over-subscription privilege, as to the number of shares of Common Stock held on behalf of each beneficial owner as of the Record Date, the aggregate number of Rights that have been exercised pursuant to the primary subscription right, whether the Rights exercised pursuant to the primary subscription right on behalf of each beneficial owner for which you are acting have been exercised in full and the number of shares of Common Stock being subscribed for pursuant to the over-subscription privilege by each beneficial owner of Rights on whose behalf you are acting.

Enclosed are copies of the following documents:

1. Prospectus;

2. Letter to the Company’s stockholders, dated [        ], 2020; and

3. A form of letter which may be sent to beneficial holders of the Company’s Common Stock.

Rights not exercised on or prior to the Expiration Date will expire as indicated in the Section entitled “The Offering—Payment for Shares” in the Prospectus.

Additional copies of the enclosed materials may be obtained from AST Fund Solutions, LLC, the information agent, toll-free at the following telephone number: (888) 628-1041.

ANY QUESTIONS OR REQUESTS FOR ASSISTANCE CONCERNING THE OFFERING SHOULD BE DIRECTED TO AST FUND SOLUTIONS, LLC, THE INFORMATION AGENT, TOLL-FREE AT THE FOLLOWING TELEPHONE NUMBER: (888) 628-1041 OR VIA EMAIL AT INFO@ASTFINANCIAL.COM.

NOTHING HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL MAKE YOU OR ANY OTHER PERSON AN AGENT OF THE COMPANY, THE DEALER-MANAGERS, THE SUBSCRIPTION AGENT, THE INFORMATION AGENT OR ANY OTHER PERSON MAKING OR DEEMED TO BE MAKING OFFERS OF THE SECURITIES ISSUABLE UPON VALID EXERCISE OF THE RIGHTS, OR AUTHORIZE YOU OR ANY OTHER PERSON TO MAKE ANY STATEMENTS ON BEHALF OF ANY OF THEM WITH RESPECT TO THE OFFERING, EXCEPT FOR STATEMENTS MADE IN THE PROSPECTUS.