Quarter given after old city is beaten (9)
I believe the answer is:
surpassed
'is beaten' is the definition.
(I've seen this before)
'quarter given after old city' is the wordplay.
'quarter' becomes 's'.
'given' becomes 'passed' ('pass' can be a synonym of 'give').
'after' says to put letters next to each other.
'old city' becomes 'ur' (ancient Sumerian city state).
'passed' put after 'ur' is 'urpassed'.
's'+'urpassed'='SURPASSED'
(Other definitions for surpassed that I've seen before include "capped" , "beaten" , "outclassed" , "Outdid" .)