Song musician at first cut from role in West Side Story (4)
I believe the answer is:
aria
'song' is the definition.
(aria is a kind of song)
'at first cut from role in west side story' is the wordplay.
'first' indicates taking the first letters.
'cut from role in west side story' becomes 'ria' (I can't justify this - if you can you should believe this answer much more).
The initial letter of 'at' is 'a'.
'a'+'ria'='ARIA'
'musician' acts as a link.
I am not very happy about this link. It may belong to another bit of the clue.
(Other definitions for aria that I've seen before include "Puccini item" , "Operatic tune" , "Type of song" , "Operatic air" , "Elaborate accompanied song for solo voice" .)