Hood, for example? Old hat originally worn around city (6)
I believe the answer is:
outlaw
'hood for example?' is the definition.
(hood is a kind of outlaw)
'old hat originally worn around city' is the wordplay.
'old hat' becomes 'out' (I've seen this before).
'originally' suggests taking the first letters.
'around' is an insertion indicator.
'city' becomes 'la' (Los Angeles).
The first letter of 'worn' is 'w'.
'out'+'w'='outw'
'outw' going around 'la' is 'OUTLAW'.
(Other definitions for outlaw that I've seen before include "Robin Hood, for example" , "Robin Hood figure?" , "Wanted criminal" , "Criminal, bandit" , "A fugitive from legal justice" .)