After purchasing a license to Test Studio, it is cumbersome to activate that purchased license while your trial license is still active. You have to manually open the folder:
C:\Users\All Users\Telerik\TESTSTUDIO (which happens to be a hidden folder BTW), delete the files in it, then restart Test Studio.

There's no mechanism provided in the UI to switch from a trial license to a purchased license. Note the Deactivate button is not present while in trial mode.