Drug finishing off naive novelist (6)
I believe the answer is:
greene
'novelist' is the definition.
(Graham Greene)
'drug finishing off naive' is the wordplay.
'drug' becomes 'e' (E is another name for ecstasy).
'finishing off' means one lot of letters go next to another (some letters finish or go after others).
'naive' becomes 'green' (similar in meaning).
'e' after 'green' is 'GREENE'.
(Other definitions for greene that I've seen before include "Graham -, English novelist" , "Graham --, British author" , "Graham --, Eng. author" , "The Quiet American author" , "Graham -, English author (Brighton Rock)" .)