Ancient Greek city with half-completed rosery (6)

I believe the answer is:

andros

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'ancient greek city' is the definition.
I know nothing about this answer so I cannot judge whether this works.

'with half-completed rosery' is the wordplay.
'with' becomes 'and'.
'half completed rosery' becomes 'ros' (I can't explain this - if you can you should believe this answer much more).
'and'+'ros'='ANDROS'

Can you help me to learn more?

(Another definition for andros that I've seen is " Is".)

I've seen this clue in The Independent.

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