Cheese not lasting long, for the most part (4)
I believe the answer is:
brie
'cheese' is the definition.
(Brie is an example)
'not lasting long for the most part' is the wordplay.
'not lasting long' becomes 'brief' (I've seen this before).
'for the most part' means to remove the last letter.
'brief' with its last letter removed is 'BRIE'.
(Other definitions for brie that I've seen before include "French cream cheese" , "Soft and creamy mild white cheese" , "cheese-producing region" , "Prov. squalid place" , "French produce" .)