Rim, lip of a cup (4)
I believe the answer is:
brim
This clue is a double definition.
'rim' is the first definition.
(synonyms)
'lip of a cup' is the second definition.
(I've seen this before)
(Other definitions for brim that I've seen before include "Top edge of a container" , "Edge around a hat" , "Circumference" , "Upper edge" , "Projecting edge of hat" .)