Drugs cop is Southern American chap with a high opinion of himself (9)
I believe the answer is:
narcissus
'chap with a high opinion of himself' is the definition.
(self-obsessed youth in Greek myth)
'drugs cop is southern american' is the wordplay.
'drugs cop' becomes 'narc' (short for narcotics agent).
'southern' becomes 's' (abbreviation).
'american' becomes 'us' (abbreviation for United States).
'narc'+'is'+'s'+'us'='NARCISSUS'
(Other definitions for narcissus that I've seen before include "Self-regarding youth" , "Beautiful youth; plant" , "Spring flower" , "Legendary egotist" , "Flower like daffodil" .)