Song, one from 'West Side Story' needing no introduction (4)
I believe the answer is:
aria
'song' is the definition.
(I know that aria is a type of song)
'one from west side story needing no introduction' is the wordplay.
'one from west side story' becomes 'Maria' (Maria is a character in West Side Story).
'needing no introduction' means to remove the first letter.
'maria' with its initial letter taken away is 'ARIA'.
(Other definitions for aria that I've seen before include "Elaborate accompanied song for solo voice" , "Air in an opera" , "Song from an opera (4)" , "selection of opera" , "Song such as "Your Tiny Hand is Frozen"" .)