Zaba (Zagrebačka banka) does not direct register shares, so you need to transfer your shares to another broker that can DRS transfer.
A popular route has been through Interactive Brokers (IBKR), as they are available internationally and can DRS transfer for $5(US). It is not apparent that any Croatian brokers that can DRS at this time.
The quickest way is to open an Interactive Broker 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 Zaba to IBKR with a Basic FOP Transfer, then from IBKR to Computershare via DRS transfer for a $5(US) fee.
How to Transfer:
Once your shares are settled in Zaba, you can start the process by emailing the bank broker departmen at Zaba, then making a Letter of Instruction with IBKR.
Write an email to: brokeri@unicreditgroup.zaba.hr.
For the subject line write: Outbound FOP transfer to IBKR.
For the message, request a transfer of your shares to IBKR, and include your Zaba account number.
Ask them to email IBKR at fop-transfer-in@interactivebrokers.com.
You should receive a reply from Zaba giving you the go ahead for the transfer. Now you can inform IBKR.
Making the Letter of Instruction with 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 UNICREDIT on the drop down list (Zaba belongs to this financial group).
For “Your Account Number at the Financial Institution" put your Zaba account number.
For “Name of Account Holder at Financial Institution“ put your full name as defined on your Zaba account.
Select the Account type (most likely individual).
Select the country of the Financial Institution from which you access Zaba, (most likely Croatia).
For the contact email put “brokeri@unicreditgroup.zaba.hr".
You have to add the asset you want to transfer, click on “Add Asset".
On the next page search which stock you'd like to transfer (GME), click on “Search".
On the next page, click on the row “GAMESTOP CORP- CLASS A / NYSE".
On the next page, define how many shares you'd like to transfer and 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. However you do not need it, as Zaba already knows to contact IBKR.
The transfer will be processed within 1-2 weeks. You will receive an email confirming that the transfer was successfully performed. If you are feeling uncertain you can call Zaba on + 385-480-544 to check on your transfer.
After your shares reach IBKR:
Now you are able to request the DRS transfer from IBKR to Computershare. To do this you can follow the guide on how to DRS transfer from IBKR (link to IBKR guide here).