Continue performing in part of London? (5)
I believe the answer is:
acton
'part of london?' is the definition.
(I've seen this before)
'continue performing' is the wordplay.
'continue' becomes 'act' (I can't justify this - if you can you should give a lot more credence to this answer).
'performing' becomes 'on' (as in being on stage).
'act'+'on'='ACTON'
'in' acts as a link.
Can you help me to learn more?
(Other definitions for acton that I've seen before include "English statesman" , "Respond in accordance with - London district" , "London area" , "somewhere in London" , "Part of the London borough of Ealing - British historian, d. 1902" .)