Take apart detective's cloak (9)
I believe the answer is:
dismantle
'take apart' is the definition.
(I know that take apart can be written as dismantle)
'detective's cloak' is the wordplay.
'detective's' becomes 'di's' (Detective Inspector).
'cloak' becomes 'mantle' (mantle is a kind of cloak).
'dis'+'mantle'='DISMANTLE'
(Other definitions for dismantle that I've seen before include "Pull to pieces" , "Take to pieces" , "Undo" , "Take apart" , "strike" .)