Girl in many a song (5)
I believe the answer is:
maria
'girl' is the definition.
'many a song' is the wordplay.
'many' becomes 'm' (Roman numeral for a thousand).
'a song' becomes 'aria' (piece of music in an opera).
'm'+'aria'='MARIA'
'in' acts as a link.
(Other definitions for maria that I've seen before include "(Of plant) become limp" , "West Side Story girl" , "Girl's name; darker moon areas" , "Italian Mary" , "Von Trapp star" .)