Bird which is not all crest (9)
I believe the answer is:
partridge
'bird' is the definition.
(I know that partridge is a bird)
'is not all crest' is the wordplay.
'is not all' becomes 'part' (I've seen this in another clue).
'crest' becomes 'ridge' (I've seen this in other clues).
'part'+'ridge'='PARTRIDGE'
'which' is the link.
(Other definitions for partridge that I've seen before include "Animal" , "early Christmas present" , "Peculiarly apt girder for the game bird" , "Flier" , "sort of quail" .)