Dash off fleetingly to get cheese (4)
I believe the answer is:
brie
'cheese' is the definition.
(I know that Brie is a type of cheese)
'dash off fleetingly' is the wordplay.
'dash' becomes 'fly' (dash can mean to fly away).
'off' is a deletion indicator (some letters taken off).
'fleetingly' becomes 'briefly' (I've seen this before).
'briefly' with 'fly' removed is 'BRIE'.
'to get' is the link.
(Other definitions for brie that I've seen before include "cheese-producing region" , "Bergamot-flavoured tea" , "Soft, creamy French cheese" , "dairy product" , "French cream cheese" .)