Destroy detective's cover (9)
I believe the answer is:
dismantle
'destroy' is the definition.
(dismantling is a kind of destroying)
'detective's cover' is the wordplay.
'detective's' becomes 'dis' (Detective Inspector).
'cover' becomes 'mantle' (mantling is a kind of covering**).
'dis'+'mantle'='DISMANTLE'
(Other definitions for dismantle that I've seen before include "Unrig" , "Undo" , "Strip down" , "Pull to pieces" , "To demolish" .)