Not the whole perimeter? (3)

I believe the answer is:

rim

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'perimeter?' is the definition.
(thesaurus)

I don't understand how the remainder of the clue works.

(Other definitions for rim that I've seen before include "Top edge" , "Edge, border" , "An edge, canyon or cup" , "Edge - lip" , "Brink" .)

I've seen this clue in the Evening Standard.

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