Slightly burn grouse primarily served during function (5)
I believe the answer is:
singe
'slightly burn' is the definition.
'grouse primarily served during function' is the wordplay.
'primarily' indicates taking the first letters.
'served during' is an insertion indicator.
'function' becomes 'sine' (mathematical function).
The initial letter of 'grouse' is 'g'.
'g' put within 'sine' is 'SINGE'.
(Other definitions for singe that I've seen before include "slight burn" , "Effect of fire" , "Result of match accident" , "Burn superficially" , "Superficial burn" .)