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Bear left, with New York to the west — this part? (8)


I believe the answer is:


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'part?' is the definition.
The definition and answer can be both locations as well as being singular nouns.
Maybe there's a link between them I don't understand?

'bear left with new york to the west' is the wordplay.
'bear' becomes 'brook' (both can mean to tolerate or endure).
'left with' becomes 'l' (common abbreviation. I am not sure about the 'with' bit.).
'new york' becomes 'ny'.
'to the west' shows that the letters should be reversed in order (letters written right to left or 'east to west').
'ny' back-to-front is 'yn'.

'this' is the link.

Can you help me to learn more?

(Other definitions for brooklyn that I've seen before include "part of Long Island?" , "New York area" , "District and bridge in New York" , "Big Apple borough" , "Beckham Jr; NY borough" .)

I've seen this clue in The Times.
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