Criminal decapitated bird (4)
I believe the answer is:
rook
'bird' is the definition.
(rook is a kind of bird)
'criminal decapitated' is the wordplay.
'criminal' becomes 'crook' ('crook' can be a synonym of 'criminal').
'decapitated' means to remove the first letter.
'crook' with its first letter removed is 'ROOK'.
(Other definitions for rook that I've seen before include "man in marginalised position, initially" , "Steal - castle" , "Man in game" , "Defraud; bird; chessman" , "Poignant, evocative" .)