Crossword Genius

Man leaves one city for another (7)

Ross

I believe the answer is:

chester

I'm a little stuck... Click here to teach me more about this clue!

'city for another' is the definition.
I can't judge whether this defines the answer.

'man leaves one' is the wordplay.
'man' becomes 'Che'.
'leaves one' becomes 'ster' (I am not sure about this - if you are sure you should believe this answer much more).
'che'+'ster'='CHESTER'

Can you help me to learn more?

(Other definitions for chester that I've seen before include "County town south of Liverpool" , "diocese" , "historic city" , "Tetchy cries (anag)" , "Walled English city" .)

I've seen this clue in The Mirror.
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