British benefit, getting hunting dog (6)
I believe the answer is:
basset
'hunting dog' is the definition.
(basset is a kind of hunting dog)
'british benefit' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in BBC).
'benefit' becomes 'asset' (I've seen this in another clue).
'b'+'asset'='BASSET'
'getting' is the link.
(Other definitions for basset that I've seen before include "Low-set hound" , "Sturdy hunting dog" , "Short-legged dog" , "GAME" , "Hare-hunting hound among beasts" .)