Murder in detective’s district (8)
I believe the answer is:
dispatch
'murder' is the definition.
(synonyms)
'detective's district' is the wordplay.
'detective's' becomes 'di's' (Detective Inspector).
'district' becomes 'patch' (patch can mean someone's local area).
'dis'+'patch'='DISPATCH'
'in' acts as a link.
(Other definitions for dispatch that I've seen before include "Execution" , "Take out" , "Kill, send off" , "making killing" , "Quickly deal with" .)