It borders on being a centre for crime (3)

I believe the answer is:

rim

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'it borders on' is the definition.
The definition suggests a singular noun which matches the answer.

'a centre for crime' is the wordplay.
'a centre for' means to look at the middle letters.
The middle of 'crime' is 'RIM'.

'being' acts as a link.

Can you help me to learn more?

(Other definitions for rim that I've seen before include "Edge, border" , "Circular outer edge" , "Curved edge" , "Raised edge of a round object" , "Edge - lip" .)

I've seen this clue in the Evening Standard.

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