Old city kindly is under pressure (8)
I believe the answer is:
urgently
'old city kindly is under pressure' is the definition.
I can't judge whether this defines the answer.
'old city kindly is under' is the wordplay.
'old city' becomes 'ur' (ancient city state).
'kindly' becomes 'gently' (I can't justify this - if you can you should give a lot more credence to this answer).
'is under' is a charade indicator (letters next to each other) (in a down clue, some letters go below others).
'ur'+'gently'='URGENTLY'
Can you help me to learn more?
(Other definitions for urgently that I've seen before include "as quickly as possible?" , "With speedy attention" , "As a matter of priority" , "Immediately, with pressing need" , "with haste" .)