Deer had fine beard (4)
I believe the answer is:
fawn
'deer' is the definition.
(fawn is a kind of deer)
'fine beard' is the wordplay.
'fine' becomes 'f' (abbreviation).
'beard' becomes 'awn' (awn is a kind of beard).
'f'+'awn'='FAWN'
'had' acts as a link.
(Other definitions for fawn that I've seen before include "Bear does, maybe" , "shade" , "Be obsequious towards young deer?" , "Light brown colour" , "Curry favour" .)