Coventry rider keen to get back after game (6)
I believe the answer is:
godiva
'coventry rider' is the definition.
(I've seen this before)
'keen to get back after game' is the wordplay.
'keen' becomes 'avid' (I've seen this in another clue).
'to get back' says the letters should be written backwards (I've seen 'getting back' mean this).
'after' is a charade indicator (letters next to each other).
'game' becomes 'go game' (go is a board game).
'avid' written backwards gives 'diva'.
'diva' put after 'go' is 'GODIVA'.
(Other definitions for godiva that I've seen before include "Coventry heroine" , "who rode bareback?" , "Lady carried bare" , "Coventry's Lady" , "Naked Coventry rider" .)