Criminal beheaded bird (4)
I believe the answer is:
rook
'bird' is the definition.
(rook is a kind of bird)
'criminal beheaded' is the wordplay.
'criminal' becomes 'crook' (synonyms).
'beheaded' means to remove the first letter (the head of the word is removed).
'crook' with its initial letter taken off is 'ROOK'.
(Other definitions for rook that I've seen before include "Chesspiece otherwise known as a castle" , "Rip off - bird" , "Crow-like bird" , "Poignant, evocative" , "man for moving" .)