Scene of mayhem in part stopped by Wild West lawman (4,3)
I believe the answer is:
bear pit
'scene of mayhem' is the definition.
'part stopped by wild west lawman' is the wordplay.
'part' becomes 'bit' (bit is a kind of part**).
'stopped by' means one lot of letters goes inside another (I've seen this in other clues).
'wild west lawman' becomes 'earp' (Wyatt Earp).
'bit' enclosing 'earp' is 'BEAR PIT'.
'in' is the link.
(Other definitions for bear pit that I've seen before include "part of the zoo" , "rowdy scene" , "rowdy place" , "Place full of aggressive, competitive types" , "Stock Exchange?" .)