Crude English crime writer's given up taking cocaine (7)
I believe the answer is:
obscene
'crude' is the definition.
(thesaurus)
'english crime writer's given up taking cocaine' is the wordplay.
'english' becomes 'e' (abbreviation).
'crime writer' becomes 'nesbo' (Norwegian crime writer Jo Nesbo).
'given up' is a reversal indicator (in a down clue, letters go up).
'taking' indicates putting letters inside.
'cocaine' becomes 'c' (drugs abbreviation).
'e'+'nesbo'='enesbo'
'enesbo' back-to-front is 'obsene'.
'obsene' going around 'c' is 'OBSCENE'.
(Other definitions for obscene that I've seen before include "Indecent, lewd" , "Sexually offensive" , "not decent" , "Lewd - offensive" , "Repugnant; indecent" .)