City backing shop that's picked up capital (3,5)
I believe the answer is:
new delhi
'capital' is the definition.
(capital of India)
'city backing shop that's picked up' is the wordplay.
'city' becomes 'wen' (historical term for a large city).
'backing' says the letters should be written backwards.
'shop' becomes 'deli' (deli is a kind of shop).
'that's picked up' shows a homophone (sound like).
'deli' is a homophone of 'delhi'.
'wen' back-to-front is 'new'.
'new'+'delhi'='NEW DELHI'
(Other definitions for new delhi that I've seen before include "Strangely, end while in India" , "Gambling establishments" , "somewhere in Asia" , "End while in India, oddly" , "big city" .)