Get rid of detective's motor vehicle department (7)
I believe the answer is:
discard
'get rid of' is the definition.
(discarding is a kind of getting rid of)
'detective's motor vehicle department' is the wordplay.
'detective's' becomes 'di's' (Detective Inspector abbreviation).
'motor vehicle' becomes 'car' (car is a kind of motor vehicle).
'department' becomes 'd' (abbreviation eg in MOD Ministry of Defence).
'dis'+'car'+'d'='DISCARD'
(Other definitions for discard that I've seen before include "Jettison" , "Get rid of" , "bin" , "Shed" , "Reject" .)