Arizona city spies vote to leave the old country (9)
I believe the answer is:
phoenicia
'old country' is the definition.
(phoenicia matches up with the definition old country)
'arizona city spies vote to leave' is the wordplay.
'arizona city' becomes 'phoenix' (capital of Arizona).
'spies' becomes 'CIA' (Central Intelligence Agency).
'vote' becomes 'x' (how votes are marked).
'to leave' suggests deleting specific letters.
'phoenix'+'cia'='phoenixcia'
'phoenixcia' with 'x' taken out is 'PHOENICIA'.
'the' acts as a link.
(Other definitions for phoenicia that I've seen before include "Ancient land in Lebanon and 5 dn" , "Middle Eastern region historically" , "Historic Middle East state" .)