A local name for European city displaying a certain atmosphere (5)
I believe the answer is:
aroma
'a certain atmosphere' is the definition.
(aroma can mean an atmosphere or quality)
'a local name for european city' is the wordplay.
'local name for european city' becomes 'Roma' (Italian name for Rome).
'a'+'roma'='AROMA'
'displaying' is the link.
(Other definitions for aroma that I've seen before include "particular charm" , "Scent - fragrance" , "Agreeable odour" , "Pervasive quality" , "Scent - smell" .)