If you typed/pasted in your Europa by Reason license number correctly in the Enter License field in the Europa by Reason splash, hit OK and nothing happens, it's probably because the macOS user you are logged in as doesn't have read & write permissions to the global Application Support/Propellerhead Software folder. To resolve this, proceed as follows:
1. Go to the /Library/Application Support folder:
2. Right click the "Propellerhead Software" folder and select "Get Info":
(If there is no "Propellerhead Software" folder there, manually create one.)
3. Click the padlock (if locked) and enter the admin password.
4. Click the plus (+) sign to add a user:
5. Select the user you are logged in as and click "Select".
6. Select the user you just added and make sure the privileges are set to "Read & Write":
Now, you should be able to authorize Europa by Reason.