Detective's area is murder (8)
I believe the answer is:
dispatch
'murder' is the definition.
('dispatch' can be a synonym of 'murder')
'detective's area' is the wordplay.
'detective's' becomes 'dis' (Detective Inspector).
'area' becomes 'patch' (patch is a kind of area**).
'dis'+'patch'='DISPATCH'
'is' acts as a link.
(Other definitions for dispatch that I've seen before include "Send (I, not E)" , "Take out" , "Send promptly; murder" , "Execution" , "report I preferred" .)