It sticks the cup up (3)
I believe the answer is:
gum
'it sticks' is the definition.
The definition suggests a singular noun which matches the answer.
'cup up' is the wordplay.
'cup' becomes 'mug' (I've seen this before).
'up' is a reversal indicator (in down clue: letters go upwards).
'mug' back-to-front is 'GUM'.
'the' acts as a link.
Can you help me to learn more?
(Other definitions for gum that I've seen before include "Leaving body" , "Sticky stuff - tree" , "Prepartion for sticking or chewing" , "surrounding roots of teeth?" , "Part of mouth; a tree" .)