Old city moving right right right (4)

I believe the answer is:

tory

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'right' is the definition.
(Tory can mean Conservative or right-wing)

I cannot understand how the rest of the clue works.

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.)" , "A British Conservative" , "Opponent of 8 Down and 14 Across, partner of 14 Down?" .)

I've seen this clue in The Guardian.

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