Expert to study din round second old city (11)
I believe the answer is:
connoisseur
'expert' is the definition.
(I know that Connoisseur is a type of expert)
'study din round second old city' is the wordplay.
'study' becomes 'con' (con can informally mean to study).
'din' becomes 'noise' (a din is a noisy disturbance).
'round' indicates putting letters inside.
'second' becomes 's' (common abbreviation).
'old city' becomes 'ur' (ancient city state).
'noise' enclosing 's' is 'noisse'.
'con'+'noisse'+'ur'='CONNOISSEUR'
'to' is the link.
(Other definitions for connoisseur that I've seen before include "Knowledgeable art-lover" , "Expert judge of taste" , "discriminating judge" .)