Continue to perform in part of West London (5)
I believe the answer is:
acton
'part of west london' is the definition.
'acton' can be an answer for 'part' (I have seen 'part of London' mean 'acton' so perhaps 'part' could also mean 'acton'). I'm not certain of the 'of west london' bit.
'continue to perform' is the wordplay.
'continue' becomes 'on' (I've seen this in other clues).
'to' says to put letters next to each other (I've seen this in other clues).
'perform' becomes 'act' (acting is a kind of performing).
'on' after 'act' is 'ACTON'.
'in' is the link.
Can you help me to learn more?
(Other definitions for acton that I've seen before include "English statesman" , "somewhere in London" , "District of West London" , "Respond in accordance with - London district" , "Part of the London borough of Ealing - British historian, d. 1902" .)