Craze in front part around old city (6)
I believe the answer is:
furore
'craze' is the definition.
('furore' can be a synonym of 'craze')
'front part around old city' is the wordplay.
'front part' becomes 'fore' (I've seen this before).
'around' is an insertion indicator.
'old city' becomes 'ur' (ancient city state).
'fore' enclosing 'ur' is 'FURORE'.
'in' is the link.
(Other definitions for furore that I've seen before include "Sudden outburst, uproar" , "An uproar of fury or enthusiasm" , "Storm" , "Hoo-ha" , "To-do" .)