Eager rise for singer (4)
I believe the answer is:
diva
'singer' is the definition.
(diva can mean a female opera singer)
'eager rise' is the wordplay.
'eager' becomes 'avid' (synonyms).
'rise' says the letters should be written backwards.
'avid' written backwards gives 'DIVA'.
'for' is the link.
(Other definitions for diva that I've seen before include "Prima dona" , "fat lady?" , "Prima donna, woman opera singer" , "Grand female singer" , "Successful lady" .)