Exhibit 99.(d)(iii)

TEKLA WORLD HEALTHCARE FUND

NOTICE TO SHAREHOLDERS WHO ARE RECORD HOLDERS

Up to [ ] Common Shares of Beneficial Interest of the Trust Issuable Upon Exercise of Non-Transferable Rights

March 8, 2021

Dear Shareholder:

Enclosed for your consideration is a prospectus, dated March [ ], 2021 (the “Prospectus”), relating to the offering by Tekla World Healthcare Fund (the “Trust”) of non-transferable subscription rights (the “Rights”) to subscribe for up to an aggregate of [ ] shares of beneficial interest of the Trust, par value $0.01 per share (the “Shares”). The Rights will be issued to shareholders of record (the “Record Date Shareholders”) as of 5:00 p.m., Eastern Time, on March 8, 2021 (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 March 16, 2021, and ends at 5:00 p.m., Eastern Time, on April 6, 2021, unless extended by the Trust in its sole discretion (the “Expiration Date”). The Rights are non-transferable. The Shares are listed on the New York Stock Exchange (“NYSE”) under the symbol “THW.”

As described in the Prospectus, each Record Date Shareholder is entitled to receive one Right for each outstanding Share owned on the Record Date. The Rights entitle the holder thereof to purchase one new Share for every three Rights held (the “Primary Subscription”) at the subscription price (the “Subscription Price”), to be calculated as described in the Prospectus as of the Expiration Date (the “Offer”). Record Date Shareholders who fully exercise their Rights pursuant to the Primary Subscription will be entitled to subscribe, on the terms and subject to the conditions set forth in the Prospectus, including proration, for additional Shares that remain unsubscribed as a result of any unexercised Rights. In addition, any non-Record Date Shareholders who exercise Rights are entitled to subscribe for remaining Shares that are not otherwise subscribed for by Record Date Shareholders pursuant to their over-subscription privileges, on the terms and subject to the conditions set forth in the Prospectus. We refer to these over-subscription privileges as the “Over-Subscription Privileges.”

The subscription price per Share (the "Subscription Price") will be determined based upon a formula equal to 95% of the volume weighted average price of a Share on the NYSE on the date on which the Offer expires, as such date may be extended from time to time, and each of the four (4) preceding trading days (the "Formula Price"). If, however, the Formula Price is less than 90% of the net asset value ("NAV") per Share at the close of trading on the NYSE on the Expiration Date, then the Subscription Price will be 90% of the Trust's NAV per Share at the close of trading on the NYSE on the Expiration Date. 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 will be paid on amounts refunded.

The Rights will be evidenced by subscription rights certificates (the “Subscription Rights Certificates”). No fractional Shares will be issued pursuant to the Rights.

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 or a notice of guaranteed delivery by the Subscription Agent.

Enclosed are copies of the following documents:

1. Prospectus;

2. Subscription Rights Certificate;

3. Instructions as to the Use of Tekla World Healthcare Fund Subscription Rights Certificates;

4. Notice of Guaranteed Delivery; and

5. A return envelope, addressed to American Stock Transfer & Trust Company, LLC.

Your prompt attention is requested. To exercise Rights, you should complete and sign the Subscription Rights Certificate and forward it, with payment of the Estimated Subscription Price in full for each Share subscribed for pursuant to the Primary Subscription and the Over-Subscription Privilege to the Subscription Agent, as indicated on the Subscription Rights Certificate and as indicated in the Prospectus. The Subscription Agent must receive the properly completed and duly executed Subscription Rights Certificate and full payment of the Estimated Subscription Price on or prior to the Expiration Date, except as otherwise indicated in the Section entitled “The Offer—Payment for Shares” in the Prospectus.

ANY QUESTIONS OR REQUESTS FOR ASSISTANCE CONCERNING THE RIGHTS OFFERING SHOULD BE DIRECTED TO AST FUND SOLUTIONS, LLC, THE INFORMATION AGENT, TOLL-FREE AT THE FOLLOWING TELEPHONE NUMBER: (866) 620-0678.