Important old city chap.. (6)
I believe the answer is:
urgent
'important' is the definition.
(I've seen this before)
'old city chap' is the wordplay.
'old city' becomes 'ur' (ancient Sumerian city state).
'chap' becomes 'gent' (both can mean a man).
'ur'+'gent'='URGENT'
(Other definitions for urgent that I've seen before include "Requiring immediate attention" , "Critical" , "Pressing, immediate" , "Pressing, imperative" , "Demanding immediate attention" .)