Killed off the vice around Los Angeles (5)
I believe the answer is:
slain
'killed' is the definition.
(slaying is a kind of killing)
'the vice around los angeles' is the wordplay.
'the vice' becomes 'sin'.
'around' means one lot of letters goes inside another.
'los angeles' becomes 'LA' (abbreviation).
'sin' placed around 'la' is 'SLAIN'.
'off' is the link.
(Other definitions for slain that I've seen before include "Slaughtered" , "Violently killed" , "Killed, murdered" , "Put to the sword" .)