Her sons cut the damaged tree (5,8)
I believe the answer is:
horse chestnut
'tree' is the definition.
(horse-chestnut is a kind of tree)
'her sons cut the damaged' is the wordplay.
'damaged' indicates an anagram.
'her'+'sons'+'cut'+'the'='hersonscutthe'
'hersonscutthe' anagrammed gives 'HORSE-CHESTNUT'.
(Other definitions for horse chestnut that I've seen before include "Could one be felled like a log" , "inedible fruit" , "Conker tree" , "Tree with sticky buds" , "Type of tree" .)