Very important old city man (6)
I believe the answer is:
urgent
'very important' is the definition.
'old city man' is the wordplay.
'old city' becomes 'ur' (ancient city state).
'man' becomes 'gent' (gent is a kind of man).
'ur'+'gent'='URGENT'
(Other definitions for urgent that I've seen before include "To be done asap" , "Needing immediate action" , "Pressing, burning" , "Extremely pressing" , "Needing early action" .)