Grin broadly after antler found in wood (8)
I believe the answer is:
hornbeam
'wood' is the definition.
(type of tree)
'grin broadly after antler' is the wordplay.
'grin broadly' becomes 'beam' (beam can mean to give a big smile).
'after' says to put letters next to each other.
'antler' becomes 'horn' (horn on a deer).
'beam' after 'horn' is 'HORNBEAM'.
'found in' is the link.
(Other definitions for hornbeam that I've seen before include "Tree good for hedging" , "white wood" , "Timber" , "heavy plant" , "Resident in wood perhaps" .)