Beak with half-cooked neck (4,3,3)
I believe the answer is:
bill and coo
'neck' is the definition.
(thesaurus)
'beak with half-cooked' is the wordplay.
'beak' becomes 'bill' (synonyms).
'with' becomes 'and'.
'half' suggests halving the letters.
'cooked' with half the letters taken is 'coo'.
'bill'+'and'+'coo'='BILL AND COO'
(Other definitions for bill and coo that I've seen before include "Cuddle and whisper amorously" , "show affection thus" .)