Conservative old city has centre overturned (4)
I believe the answer is:
tory
'conservative' is the definition.
(informal term for a Conservative Party member)
'old city has centre overturned' is the wordplay.
I cannot really understand how this works, but
'old' could be 'o' (abbreviation) and 'o' is present in the answer.
The remaining letters 'try' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for tory that I've seen before include "English Conservative politician or Donegal island" , "Traditionalist" , "Politician; tyro (anag.)" , "Opponent of 8 Down and 14 Across, partner of 14 Down?" , "A British Conservative" .)