From what we hear, deserve to get the bird (4)
I believe the answer is:
erne
'the bird' is the definition.
(erne is a kind of bird)
'from what we hear deserve' is the wordplay.
'from what we hear' shows a homophone (sound like).
'deserve' becomes 'earn' (I've seen this before).
'earn' is a homophone of 'ERNE'.
'to get' acts as a link.
(Other definitions for erne that I've seen before include "Fish-eating sea eagle" , "flyer in the main" , "Irish lough" , "Irish river - sea eagle" , "A high-flier" .)