Detectives chasing - managed to get off! (6)
I believe the answer is:
rancid
'off' is the definition.
(thesaurus)
'detectives chasing managed' is the wordplay.
'detectives' becomes 'cid'.
'chasing' says to put letters next to each other.
'managed' becomes 'ran' (I've seen this before).
'cid' put after 'ran' is 'RANCID'.
'to get' acts as a link.
(Other definitions for rancid that I've seen before include "No longer fresh" , "Smelling or tasting of stale fat" , "Noxious" , "(Of fats) stale" , "Sour like stale fat" .)