Line the writer grasps when climbing tree (3)
I believe the answer is:
elm
'tree' is the definition.
(elm tree is a kind of tree)
'line the writer grasps when climbing' is the wordplay.
'line' becomes 'l' (used when specifying particular lines from a poem).
'the writer' becomes 'me' (the person who wrote the clues).
'grasps' means one lot of letters goes inside another (inserted letters are held or grasped).
'when climbing' shows that the letters should be reversed in order (in a down clue, letters go up).
'l' put into 'me' is 'mle'.
'mle' backwards is 'ELM'.
(Other definitions for elm that I've seen before include "Furniture wood" , "Kind of tree" , "one has a trunk and leaves" , "Native British tree" , "Tree with winged fruit" .)