Bird's very big quarry (6)
I believe the answer is:
osprey
'bird's' is the definition.
(osprey is a kind of bird)
'very big quarry' is the wordplay.
'very big' becomes 'os' (abbreviation for outsize).
'quarry' becomes 'prey' ('prey' can be a synonym of 'quarry').
'os'+'prey'='OSPREY'
(Other definitions for osprey that I've seen before include "Bird of fine feather" , "predatory bird" , "Fish eagle" , "I grab fish" , "A feather trimming (6)" .)