Conservative: I win having lost Conservative city (5)
I believe the answer is:
civic
'city' is the definition.
(I've seen this before)
'conservative i win having lost conservative' is the wordplay.
'conservative i' becomes 'ci' (this could be a standard abbreviation which I don't know about).
'win' becomes 'victory' (a win is a victory).
'having lost' indicates named letters should be taken away.
'conservative' becomes 'tory' (informal term for a Conservative Party member).
'victory' with 'tory' removed is 'vic'.
'ci'+'vic'='CIVIC'
Can you help me to learn more?
(Other definitions for civic that I've seen before include "Relating to citizens" , "Like, eg, town councils" , "Relating to citizenship or public affairs" , "view of the city" , "Relating to a city/town" .)