Bear damaging tree a lot (8)
I believe the answer is:
tolerate
'bear' is the definition.
(synonyms)
'damaging tree a lot' is the wordplay.
'damaging' indicates anagramming the letters.
'tree'+'a'+'lot'='treealot'
'treealot' with letters rearranged gives 'TOLERATE'.
(Other definitions for tolerate that I've seen before include "Accept or bear with" , "Put up with, permit without protest" , "Endure with forbearance" , "Suffer" , "Brook" .)