Eye-opener behind damaged palm tree (5)
I believe the answer is:
maple
'tree' is the definition.
(maple is a kind of tree)
'eye-opener behind damaged palm' is the wordplay.
'opener' says to take the initial letters.
'behind' means one lot of letters go next to another.
'damaged' is an anagram indicator.
The initial letter of 'eye' is 'e'.
'palm' is an anagram of 'mapl'.
'e' after 'mapl' is 'MAPLE'.
(Other definitions for maple that I've seen before include "Tree whose leaf features on the flag of Canada" , "Tree; sauce" , "Tree; sugar from it" , "Syrup-yielding tree" , "Tree with winged seeds" .)