Old city man is earnest and persistent (6)
I believe the answer is:
urgent
'persistent' is the definition.
(thesaurus)
'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'
'is earnest and' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for urgent that I've seen before include "Requiring immediate attention" , "Pressing, burning" , "Critical" , "Pressing, immediate" , "Pressing, imperative" .)