Finish off the henhouse for Bill's partner (3)
I believe the answer is:
coo
'bill's partner' is the definition.
(I've seen this in another clue)
'finish off the henhouse' is the wordplay.
'finish off' means to remove the last letter.
'the henhouse' becomes 'coop' (synonyms).
'coop' with its last letter taken off is 'COO'.
'for' is the link.
(Other definitions for coo that I've seen before include "Sound made by a pigeon" , "Sound coming from dovecote" , "Murmur amorously" , "Sound like a dove" , "I'm surprised" .)