Shot round the circuit in the city (4)
I believe the answer is:
troy
'the city' is the definition.
(Troy is an example)
'shot round the circuit' is the wordplay.
'shot' becomes 'try' (I've seen this in another clue).
'round' indicates putting letters inside.
'the circuit' becomes 'o'.
'try' placed around 'o' is 'TROY'.
'in' acts as a link.
(Other definitions for troy that I've seen before include "Ancient city where fair Helen was a captive" , "Ancient city in Asia Minor" , "Ancient city; type of weight" , "Priam's city" , "City destroyed" .)