Old city fellow's emergency (6)
I believe the answer is:
urgent
'emergency' is the definition.
(thesaurus)
'old city fellow's' is the wordplay.
'old city' becomes 'ur' (ancient city state).
'fellow' becomes 'gent' ('gent' can be a synonym of 'fellow').
'ur'+'gent'='URGENT'
(Other definitions for urgent that I've seen before include "demanding speedy action" , "Pressing, imperative" , "Requiring immediate attention" , "Demanding immediate attention" , "Pressing, compelling" .)