British graduate goes round old city in old country (5)
I believe the answer is:
burma
'old country' is the definition.
(I've seen this before)
'british graduate goes round old city' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'graduate' becomes 'MA' (abbreviation for Master of Arts).
'goes round' is an insertion indicator.
'old city' becomes 'ur' (ancient city state).
'b'+'ma'='bma'
'bma' placed around 'ur' is 'BURMA'.
'in' is the link.
(Other definitions for burma that I've seen before include "Another name for Myanmar" , "SE Asian country" , "Union of Myanmar" , "Country also known as Myanmar" , "Country whose name was changed to Myanmar in 1989" .)