Beam and grate left unfinished (4)
I believe the answer is:
grin
'beam' is the definition.
(I've seen this before)
'grate left unfinished' is the wordplay.
'grate' becomes 'grind' (synonyms).
'left unfinished' means to remove the last letter.
'grind' with its final letter taken away is 'GRIN'.
'and' is the link.
(Other definitions for grin that I've seen before include "11 smile" , "Cheesy smile?" , "Beam" , "Happy expression" , "Look pleased" .)