If youre staying in Croatia for less than 3 months and you want to operate as 9A/HOME_CALL the only thing you need is your CEPT licence.
If you wish to obtain Croatian callsign (9A), you need to do the following three steps:
1. Obtain personal identification number (OIB)
A place to start is Croatian tax administration who is in charge of issuing personal identification numbers (OIB). You can find all needed information on their website: http://www.porezna-uprava.hr/HR_OIB/Stranice/DodjeljivanjeOIBa.aspx. Also, they have an english version of the procedure prepared for foreigners: http://www.porezna-uprava.hr/HR_OIB/Documents/oib%20dokumentacija%20-en%20(2).pdf.
You will need to fill an Application form for the determination and assignment of PIN (OIB) and you will have to bring your passport. If the Application is submitted by an agent acting in the name of a foreign entity (natural or legal), besides the above mentioned documents (document copies), they shall also submit a power of attorney. This is usefull if youre not able to come to the tax administration yourself, but remember that all the documents need to be in Croatian, as it is the official language in Croatia.
2. Apply for a callsign
Croatian Amateur Radio Association is in charge for issuing a callsign proposal. Since 2017. the rules for domestic and foreign radioamateurs are the same. You can find the Rules under the “Documents” section of this website (or by clicking here) and see which callsigns you can get, as well as what terms and conditions apply.
Application form itself does not exist: its enough to send a written request with attached CEPT licence and the document showing your OIB (from the step 1). Based on your amateur radio class, you will get a 3-letter-suffix callsign from the 9A3 or 9A5 range. If you want a different callsign, check the rules about how to get it.
This request is a subject to a small fee for handling the request and issuing the callsign proposal.
3. Apply for a licence
Once you have a callsign proposal, you have one final step to do: get a transmit permit which is issued by a Croatian regulatory agency for network activities. Basicaly, you need to fill out a form, attach the documents from steps 1 and 2. Website explaining the latest information is this one: https://www.hakom.hr/default.aspx?id=348.