Continue to perform in London (5)
I believe the answer is:
acton
'in london' is the definition.
(area of London)
'continue to perform' is the wordplay.
'continue' becomes 'on' (I've seen this in other clues).
'to' is a charade indicator (letters next to each other) (I've seen this in other clues).
'perform' becomes 'act' (acting is a kind of performing).
'on' put after 'act' is 'ACTON'.
(Other definitions for acton that I've seen before include "somewhere in London" , "Respond in accordance with - London district" , "part of London on the tube" , "District of West London" , "London area" .)