Score the finest music, 'Messiah' last of all (4)
I believe the answer is:
etch
'score' is the definition.
(etch can mean to score or carve into something)
'the finest music messiah last of all' is the wordplay.
'last of all' says to take the final letters.
The last letters of 'the finest music messiah' are 'ETCH'.
(Other definitions for etch that I've seen before include "Make deep lines" , "Make carvings" , "Carve (design) on a surface" , "Carve into metal with acid" , "What most engravers presumably find easy to do" .)