A city girl cut back on costs (9)

I believe the answer is:

annapolis

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'a city' is the definition.
(I know that Annapolis is or was a state capital)

'girl cut back on costs' is the wordplay.
'girl' becomes 'Anna'.
'cut back on costs' becomes 'polis' (I can't explain this - if you can you should give a lot more credence to this answer).
'anna'+'polis'='ANNAPOLIS'

Can you help me to learn more?

(Other definitions for annapolis that I've seen before include "US city" , "Capital of Maryland" , "US state capital" .)

I've seen this clue in The Daily Express.

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