Group fails to finish search (4)
I believe the answer is:
comb
'search' is the definition.
(I know that comb is a more specific form of search)
'group fails to finish' is the wordplay.
'group' becomes 'combo' (a combo can mean a musical group).
'fails to finish' means to remove the last letter.
'combo' with its final letter taken away is 'COMB'.
(Other definitions for comb that I've seen before include "Systematically search" , "business storage unit" , "Barber's implement" , "Search methodically" , "Device for tidying one's appearance" .)