Keen to back singer (4)
I believe the answer is:
avid
'keen' is the definition.
(I've seen this in other clues)
'back singer' is the wordplay.
'back' says the letters should be written backwards.
'singer' becomes 'diva' (diva can mean a female opera singer).
'diva' backwards is 'AVID'.
'to' acts as a link.
(Other definitions for avid that I've seen before include "'Eager, enthusiastic (4)'" , "Extremely enthusiastic" , "Showing active interest and enthusiasm" , "Fanatical" , "'Eager, zealous (4)'" .)