A singer eager to make a comeback (4)
I believe the answer is:
diva
'a singer' is the definition.
(diva can mean a female opera singer)
'eager to make a comeback' is the wordplay.
'eager' becomes 'avid' (synonyms).
'to make a comeback' says the letters should be written in reverse (I've seen 'making a comeback' mean this).
'avid' backwards is 'DIVA'.
(Other definitions for diva that I've seen before include "Successful lady" , "Female opera star" , "For example Sutherland" , "Distinguished female singer" , "High-maintenance opera singer?" .)