The problem is "rental" is already taken for things like 3-day or 7-day or whatever rentals. Reusing the term would cause even greater confusion.

"Buy license" or "License" (as a verb, although it's ambiguous in English) is more accurate... but that still doesn't tell you any of the fine print, so I'm not sure it does any good at all. (After all, anyone who cares at all about this stuff already knows it's a license, and doesn't need to be told.)

In a case like this, how the heck are you supposed to know that whether or not your license continues is dependent upon whether or not Sony and Warner Bros. can come to an agreement to renew it?