This hoodlum is left out (4)
I believe the answer is:
lout
'this hoodlum' is the definition.
(both can mean a violent youth)
'left out' is the wordplay.
'left' becomes 'l' (common abbreviation).
'l'+'out'='LOUT'
'is' acts as a link.
(Other definitions for lout that I've seen before include "thug!" , "Yobbo" , "Yob" , "Boor, roughneck" , "Antisocial person" .)