Cup part (4)
(Other definitions for handle that I've seen before include "Part to be grasped" , "Touch - deal with" , "Feel or manipulate" , "Cope with" , "Manage or deal with - in manual way?" .)
'cup part' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for brim that I've seen before include "Projecting edge of hat" , "Top edge of a container" , "Upper edge" , "'Edge, like that of a hat (4)'" , "The edge of a cup or glass" .)