Sticking at home, tucking into drink (6)
I believe the answer is:
gluing
'sticking' is the definition.
(I've seen this before)
'home tucking into drink' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'tucking into' indicates putting letters inside.
'drink' becomes 'glug' (I've seen this before).
'in' inserted within 'glug' is 'GLUING'.
'at' acts as a link.
(Other definitions for gluing that I've seen before include "Pasting" , "Sticking" .)