Bird doesn't finish making bird sound (3)
I believe the answer is:
'bird sound' is the definition.
'bird doesn't finish' is the wordplay.
'bird' becomes 'coot' (coot is a kind of bird).
'doesn't finish' means to remove the last letter.
'coot' with its last letter taken away is 'COO'.
'making' is the link.
(Other definitions for coo that I've seen before include "Pigeon's sound" , "Sound made by doves" , "Make loving sounds -bill and . . ." , "Bill's companion" , "crumbs" .)