Two different lives next to quality city (8)
I believe the answer is:
belgrade
'city' is the definition.
(capital of Serbia)
'two different lives next to quality' is the wordplay.
'two different lives' becomes 'bel' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'next to' means one lot of letters go next to another.
'quality' becomes 'grade ' (I've seen this before).
'bel'+'grade'='BELGRADE'
(Other definitions for belgrade that I've seen before include "Serbian capital" , "Foreign capital" , "It was Byzantine" , "In foreign city" , "Capital of Serbia and Montenegro" .)