Slippery around rim (3)
I believe the answer is:
lip
'rim' is the definition.
(both can mean the edge of something)
'slippery around' is the wordplay.
'around' indicates the answer is hidden within the clue.
'LIP' is hidden within 'slippery'.
(Other definitions for lip that I've seen before include "Fleshy fold of mouth tissue" , "Brim" , "Edge; impudent talk" , "Part of mouth or cheek" , "Rim; impertinence" .)