Continue to play a part in part of London (5)
I believe the answer is:
acton
'part of london' is the definition.
(I've seen this before)
'continue to play a part' 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).
'play a part' becomes 'act' (I've seen this before).
'on' put after 'act' is 'ACTON'.
'in' acts as a link.
(Other definitions for acton that I've seen before include "Respond in accordance with - London district" , "London area" , "Part of the London borough of Ealing - British historian, d. 1902" , "Gladstone's adviser" , "part of London on the tube" .)