Old PM is with artist entering exotic food shop (8)
I believe the answer is:
disraeli
'old pm' is the definition.
(Benjamin Disraeli, Victorian prime minister)
'is with artist entering exotic food shop' is the wordplay.
'with' means one lot of letters go next to another.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'entering' indicates putting letters inside.
'exotic food shop' becomes 'deli' (I've seen this before).
'is'+'ra'='isra'
'isra' placed into 'deli' is 'DISRAELI'.
(Other definitions for disraeli that I've seen before include "Queen Victoria's favourite prime minister, d. 1881" , "Victorian statesman" , "Victorian politician" , "PM, bought Suez Canal" , "Benjamin --, former PM" .)