Trains once operating cross part of New York (5)

I believe the answer is:

bronx

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'part of new york' is the definition.
('Bronx' is part of 'new york')

'trains once operating cross' is the wordplay.
'trains once' becomes 'br' (I am not sure about the 'once' bit.).
'operating' becomes 'on' (I've seen this in other clues).
'cross' becomes 'x' (X is cross-shaped).
'br'+'on'+'x'='BRONX'

Can you help me to learn more?

(Other definitions for bronx that I've seen before include "District of New York" , "Part of New York City" , "New York City borough" .)

I've seen this clue in The Times.

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