Cheese crisp? Not quite (4)
I believe the answer is:
brie
'cheese' is the definition.
(I've seen this before)
'crisp? not quite' is the wordplay.
'crisp?' becomes 'brief' ('brief' can be a synonym of 'crisp').
'not quite' means to remove the last letter.
'brief' with its final letter removed is 'BRIE'.
(Other definitions for brie that I've seen before include "Round soft Fr. cheese" , "French produce" , "Prov. squalid place" , "cheese-producing region" , "Food" .)