Songwriter is honed after working on first of musicals (8)
I believe the answer is:
sondheim
'songwriter' is the definition.
(Stephen Sondheim, 1930-2021)
'is honed after working on first of musicals' is the wordplay.
'after working' indicates anagramming the letters.
'on' is a charade indicator (letters next to each other).
'first of musicals' becomes 'm' (1st letter of 'musicals').
'is'+'honed'='ishoned'
'ishoned' anagrammed gives 'sondhei'.
'sondhei'+'m'='SONDHEIM'
(Other definitions for sondheim that I've seen before include "Stephen --, US composer and lyricist" , "West Side Story lyricist" .)