Adhesive for a broken mug (3)
I believe the answer is:
gum
'adhesive' is the definition.
(gum is a kind of adhesive)
'a broken mug' is the wordplay.
'a broken' is an anagram indicator.
'mug' with letters rearranged gives 'GUM'.
'for' is the link.
(Other definitions for gum that I've seen before include "Chewed sweet" , "Stuff to chew" , "Glue; jelly-like sweet" , "Sticky plant substance" , "seal" .)