A bird damaged her fencing (10)
I believe the answer is:
'a bird' is the definition.
(type of bird)
'damaged her fencing' is the wordplay.
'damaged' indicates an anagram.
'herfencing' is an anagram of 'GREENFINCH'.
(Other definitions for greenfinch that I've seen before include "Winger" , "Seed-eating songbird" , "Large seed-eater" , "Her fencing (anag.)" , "bird" .)