Charm a woman with a little time at old city (7)
I believe the answer is:
enamour
'charm' is the definition.
(I know that charm can be written as enamour)
'a woman with a little time at old city' is the wordplay.
'a woman' becomes 'ena' (feminine given name).
'with' says to put letters next to each other.
'a little time' becomes 'mo' (short period of time).
'at' says to put letters next to each other.
'old city' becomes 'ur' (ancient city state).
'ena'+'mo'+'ur'='ENAMOUR'
(Other definitions for enamour that I've seen before include "Fill with love" , "sweep one off one's feet" , "Enchant" , "entrance" , "Charm, captivate" .)