Row with a city girl (7)

I believe the answer is:

tiffany

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

'girl' is the definition.

'row with a city' is the wordplay.
'row with' becomes 'tiff' (tiff is a kind of row. I am not sure about the 'with' bit.**).
'city' becomes 'ny' (I've seen this in other clues).
'tiff'+'a'+'ny'='TIFFANY'

Can you help me to learn more?

(Other definitions for tiffany that I've seen before include "Transparent" , "like a sort of glass" , "fine fabric" , "US glass designer" , "Girl's name - New York jeweller" .)

I've seen this clue in The Independent.

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