Pressing very old city guy (6)
I believe the answer is:
urgent
'pressing' is the definition.
(synonyms)
'very old city guy' is the wordplay.
'very old city' becomes 'ur' (ancient Mesopotamian city).
'guy' becomes 'gent' (I've seen this in another clue).
'ur'+'gent'='URGENT'
(Other definitions for urgent that I've seen before include "grave?" , "Requiring immediate attention" , "Pressing, imperative" , "Extremely pressing" , "demanding speedy action" .)