Grimy around edge (3)
I believe the answer is:
rim
'edge' is the definition.
(I know that rim is a type of edge)
'grimy around' is the wordplay.
'around' indicates a hidden word.
'RIM' is hidden within 'grimy'.
(Other definitions for rim that I've seen before include "Edge - lip" , "Edge or margin" , "Curved edge" , "Raised edge of a round object" , "Edge, border" .)