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