Off one rushed, to the police (6)
I believe the answer is:
rancid
'off' is the definition.
(I've seen this before)
'one rushed to the police' is the wordplay.
'one rushed' becomes 'ran'.
'to the police' becomes 'CID' (abbreviation for Criminal Investigation Department).
'ran'+'cid'='RANCID'
(Other definitions for rancid that I've seen before include "Turned -- malodorous" , "Stale, with an offensive smell" , "Smelling bad like stale fat" , "Turned - foul-smelling" , "Rank-smelling." .)