...before detectives tore off (6)
I believe the answer is:
rancid
'off' is the definition.
(thesaurus)
'before detectives tore' is the wordplay.
'before' is a charade indicator (letters next to each other).
'detectives' becomes 'cid'.
'tore' becomes 'ran' (I've seen this before).
'cid' put after 'ran' is 'RANCID'.
(Other definitions for rancid that I've seen before include "Noxious" , "Rotten; high" , "(Of fat/oil) stale and foul smelling" , "Stale, rank" , "(Of butter) gone off" .)