Feel nostalgia for old, old city island state (8)
I believe the answer is:
missouri
'state' is the definition.
(Missouri is an example)
'feel nostalgia for old old city island' is the wordplay.
'feel nostalgia for' becomes 'miss' (I've seen this in another clue).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'old city' becomes 'ur' (ancient city state).
'island' becomes 'i' (geographical abbreviation).
'miss'+'o'+'ur'+'i'='MISSOURI'
(Other definitions for missouri that I've seen before include "Biggest tributary of the Mississippi" , "State south of Iowa" , "River nicknamed Big Muddy" , "State of central USA" , "US river - state" .)