Exhibit (a)(1)(iv)

OFFER BY

INVESCO SENIOR INCOME TRUST

TO PURCHASE FOR CASH UP

TO 15% OF ITS SHARES FOR 98.5%

OF NET ASSET VALUE

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT

11:59 P.M., NEW YORK CITY TIME, ON DECEMBER 5, 2019

(“EXPIRATION DATE”), UNLESS EXTENDED

THIS OFFER IS NOT CONDITIONED ON ANY MINIMUM NUMBER OF SHARES BEING

TENDERED, BUT IS SUBJECT TO OTHER CONDITIONS AS OUTLINED IN THE OFFER

TO PURCHASE AND IN THE LETTER OF TRANSMITTAL.

November 1, 2019

To Our Clients:

Enclosed for your consideration is the Offer to Purchase, dated November 1, 2019, of Invesco Senior Income Trust (the “Fund”), and a related Letter of Transmittal. Together these documents constitute the “Offer.” The Fund is offering to purchase up to 15% of its outstanding Common Shares (the “Shares”), upon the terms and subject to the conditions set forth in the Offer.

A tender of your Shares can be made only by us as the registered holder and only pursuant to your Instructions. The Offer to Purchase and the Letter of Transmittal are being sent to you for your information only. They cannot be used by you to tender Shares held by us for your account. We are the registered holder of Shares held for your account.

Your attention is called to the following:

(1) The purchase price to be paid for the Shares is an amount per Share, net to the seller in cash, equal to 98.5% of the net asset value per Share (“NAV”) in U.S. dollars per Share as determined by the Fund as of the close of ordinary trading on the New York Stock Exchange on December 6, 2019, unless otherwise extended. The current NAV of the Fund will be calculated daily and may be obtained by calling AST Fund Solutions, LLC, the Fund’s Information Agent, toll free at: 866 796-6869.

(2) The Offer is not conditioned upon any minimum number of Shares being tendered.

(3) Upon the terms and subject to the conditions of the Offer, the Fund will purchase all Shares validly tendered (and not withdrawn) on or prior to the Expiration Date, provided that the total number of Shares tendered does not exceed 15% of the Fund’s outstanding Shares. In the event that more than 15% of the Fund’s outstanding Shares are tendered, the Fund will purchase 15% of the Fund’s outstanding Shares on a pro rata basis.

(4) Tendering shareholders will not be obligated to pay stock transfer taxes on the purchase of Shares by the Fund pursuant to the Offer, except in the instances described in Section 4, “Payment for Shares,” of the Offer to Purchase.

(5) Your instructions to us should be forwarded in ample time before the Expiration Date to permit us to submit a tender on your behalf.

If you wish to have us tender any or all of your Shares, please so instruct us by completing, executing and returning to us the instruction form set forth below. An envelope to return your instructions to us is enclosed. If you authorize the tender of your Shares, all such Shares will be tendered unless otherwise specified below. Your instructions to us should be forwarded as promptly as possible in order to permit us to submit a tender on your behalf in accordance with the terms and conditions of the Offer.

The Offer is not being made to, nor will tenders be accepted from or on behalf of, holders of Shares in any jurisdiction in which the making or acceptance of the Offer would not be in compliance with applicable law.

Neither the Fund nor its Board of Trustees is making any recommendation to any shareholder whether to tender or refrain from tendering Shares in the Offer. Each shareholder is urged to read and evaluate the Offer and accompanying materials carefully.

INSTRUCTIONS

The undersigned acknowledge(s) receipt of our letter, the enclosed Offer to Purchase dated November 1, 2019, and the Letter of Transmittal, relating to the Fund’s purchase of up to 15% of its outstanding Shares at 98.5% of the NAV.

The undersigned instructs us to tender to the Fund the number of Shares indicated below (which are held by us for the account of the undersigned), upon the terms and subject to the conditions set forth in the Offer to Purchase and in the related Letter of Transmittal that we have furnished to the undersigned.

AGGREGATE NUMBER OF SHARES TO BE TENDERED:

□ All Shares held for the undersigned;

or

□ _______ Shares (Enter number of Shares to be tendered).

PLEASE SIGN HERE
Dated: _______________, 2019
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