Large bird goes after black dog (6)
I believe the answer is:
beagle
'dog' is the definition.
(beagle is a kind of dog)
'large bird goes after black' is the wordplay.
'large bird' becomes 'eagle' (eagles are large birds).
'goes after' means one lot of letters go next to another.
'black' becomes 'b' (abbreviation as in pencil classifications).
'eagle' after 'b' is 'BEAGLE'.
(Other definitions for beagle that I've seen before include "Small hunting dog" , "hunting animal with smooth coat" , "Hunting dog followed on foot" , "Hunting hound" , "Small short-legged hound" .)