Something enjoyed but not at once (8,5)
I believe the answer is:
acquired taste
'something enjoyed but not at once' is the definition.
(a taste that takes a while to acquire)
This is all the clue.
(Other definitions for acquired taste that I've seen before include "Item not immediately appreciated" , "It's something you may come to like" , "you might not like it initially" , "Something one grows to like" , "Liking for something that comes only after experience" .)