Old city chap, desperate (6)
I believe the answer is:
urgent
'desperate' is the definition.
(thesaurus)
'old city chap' is the wordplay.
'old city' becomes 'ur' (ancient city state).
'chap' becomes 'gent' (I've seen this in other clues**).
'ur'+'gent'='URGENT'
(Other definitions for urgent that I've seen before include "Of immediate importance" , "Pressing, compelling" , "Requiring immediate action" , "Calling for immediate attention" , "Requiring immediate attention" .)