Hargreaves Lansdown does not direct register shares, so you need to transfer your shares to another broker that can do a DRS transfer. A popular route has been through Interactive Brokers (IBKR).
The quickest way is to open an IBKR account, buy a share, and request a DRS transfer (link to guide here). While you wait for your Computershare account to be created, you can transfer your shares from Hargreaves Lansdown to IBKR with a Basic FOP Transfer (free). Then from IBKR to Computershare via DRS transfer for a $5(US) fee.
How to Transfer:
You need to create a Letter of Instruction, to do this you need to submit a transfer request with the receiving broker (IBKR).
Login in your IBKR account, and click on “Transfer & Pay” from the top menu and select “Transfer Positions”.
On the next page select “Incoming”.
On the next page select “All Other Regions” from the drop down menu.
On the next page select “Basic FOP Transfer".
Select HARGREAVES LANSDOWN on the drop down list.
Put your HL account number on the field : “Your Account Number at the Financial Institution".
Choose your account type (most likely individual).
Put the Country “United Kingdom”.
Put the Contact Email email@example.com.
You have to add the asset you want to transfer, click on “Add Asset".
In the pop up window, search which stock you'd like to transfer (GME). Then click on “Search".
On the next page, click on the row “GAMESTOP CORP-CLASS A / NYSE".
Put how many shares you'd like to transfer Click on “Save and Finish".
On the next page you'll see a summary of the transfer. Write in your name as it shows on the page and click on “Continue”.
Interactive Brokers will then generate a Letter of Instruction for you. Click on “View Form”, then click on “Print”.
Print, sign, and scan the form back in.
Once the Letter of Instruction is signed, and scanned in- send an email to firstname.lastname@example.org.
For the subject write: “(Your HL Client Number) - Transfer out Request”.
For the email write: “Please see the attached Letter of Instruction as authorization for my request to transfer the securities held in my Fund & Share account (or Stocks and Shares ISA) to my Interactive Brokers account".
Attach the Letter of Instruction.
The transfer should be performed in 5-15 business days. You will receive an email confirming that the transfer was successfully performed.
After your shares reach IBKR:
Now you are able to request the DRS transfer from IBKR to Computershare. To do this you can follow our guide on how to DRS transfer from IBKR (link to guide here).