By oneself, holding hat for gangster (2,6)
I believe the answer is:
al capone
'gangster' is the definition.
(US gangster)
'by oneself holding hat' is the wordplay.
'by oneself' becomes 'alone' (being by oneself is being alone).
'holding' indicates putting letters inside.
'hat' becomes 'cap' (I've seen this in another clue).
'alone' enclosing 'cap' is 'AL CAPONE'.
'for' is the link.
(Other definitions for al capone that I've seen before include "Chicago gangster known as Scarface" , "Notorious Chicago gangster called Scarface" , "Famous gangster" , "Hood" , "Notorious gangster, d. 1947" .)