Mug went back for glue (3)
I believe the answer is:
gum
'glue' is the definition.
(I know that glue can be written as gum)
'mug went back' is the wordplay.
'went back' says the letters should be written backwards.
'mug' written backwards gives 'GUM'.
'for' is the link.
(Other definitions for gum that I've seen before include "surrounding roots of teeth?" , "Eg, a eucalyptus" , "Part of mouth; a tree" , "Leaving body" , "Glue; jelly-like sweet" .)