Later, going back round half city to the performance (7)
I believe the answer is:
recital
'the performance' is the definition.
(recital is a kind of performance)
'later going back round half city' is the wordplay.
'going back' shows that the letters should be reversed in order.
'round' means one lot of letters goes inside another.
'half' suggests halving the letters.
'later' back-to-front is 'retal'.
'city' halved is 'ci'.
'retal' placed around 'ci' is 'RECITAL'.
'to' is the link.
(Other definitions for recital that I've seen before include "Chamber music concert" , "Narration" , "Concert performed by a solo musician" , "(Usually solo) concert" , "Reading" .)