Novelist Graham __ (6)
I believe the answer is:
'novelist graham' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for greene that I've seen before include "Graham -, English novelist" , "Graham -, English author (Brighton Rock)" , "Graham -, twentieth century English author" , "The Quiet American author" , "Graham --, Eng. author" .)