Grimy around the edge (3)

I believe the answer is:

rim

'the edge' is the definition.
(rim is a kind of edge)

'grimy around' is the wordplay.
'around' says the answer is hidden in the clue.
'RIM' is hidden in the letters of 'grimy'.

(Other definitions for rim that I've seen before include "Upper or outer edge" , "Raised edge of a round object" , "Circumference" , "Outer edge of a wheel" , "Curved edge" .)

I've seen this clue in The Mirror.

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