A puzzle served half after a meal (6)
I believe the answer is:
teaser
'a puzzle' is the definition.
(I know that puzzle can be written as teaser)
'served half after a meal' is the wordplay.
'half' means to take half the letters.
'after' is a charade indicator (letters next to each other).
'a meal' becomes 'tea' (tea is a type of meal).
'served' cut in half is 'ser'.
'ser' after 'tea' is 'TEASER'.
(Other definitions for teaser that I've seen before include "A difficult problem of Teresa" , "one using a backcomb" , "Puzzling question or gentle goader" , "inducement" , "Tricky question; intriguing preliminary advert" .)