London area's one mistake? Chasing game (7)
I believe the answer is:
ruislip
'london area's' is the definition.
(Ruislip is an area of London)
'one mistake? chasing game' is the wordplay.
'one' becomes 'I' (Roman numeral).
'mistake?' becomes 'slip' (a slip is a blunder or mistake).
'chasing' is a charade indicator (letters next to each other) (some letters chase after others).
'game' becomes 'RU' (rugby union).
'i'+'slip'='islip'
'islip' after 'ru' is 'RUISLIP'.
(Other definitions for ruislip that I've seen before include "6D 5A [TUBE STATION]" , "Town west of Harrow" , "place in Metroland" .)