Old City man politely pressing (6)

I believe the answer is:

urgent

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'pressing' is the definition.
(I know that pressing can be written as urgent)

'old city man politely' is the wordplay.
'old city' becomes 'ur' (ancient city state).
'man politely' becomes 'gent' (gent is a kind of man. I am not sure about the 'politely' bit.).
'ur'+'gent'='URGENT'

Can you help me to learn more?

(Other definitions for urgent that I've seen before include "Requiring immediate action" , "Requiring early action" , "Extremely pressing" , "To be done asap" , "Needing immediate attention, don't delay" .)

I've seen this clue in The Times.

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