Celebrated singer eager to return (4)
I believe the answer is:
diva
'celebrated singer' is the definition.
'eager to return' is the wordplay.
'eager' becomes 'avid' ('avid' can be a synonym of 'eager').
'to return' says the letters should be written in reverse.
'avid' backwards is 'DIVA'.
(Other definitions for diva that I've seen before include "Callas, say" , "Female opera star" , "demanding woman" , "For example Sutherland" , "Top opera singer" .)