Visit a non-drinker last (6)
I believe the answer is:
attend
'visit' is the definition.
(I've seen this before)
'a non-drinker last' is the wordplay.
'non drinker' becomes 'tt' (Teetotaller abbreviation).
'last' becomes 'end'.
'a'+'tt'+'end'='ATTEND'
(Other definitions for attend that I've seen before include "Listen carefully" , "Be present at (an event)" , "Being 16 [LISTEN]" , "Wait upon or be present" , "Escort (someone)" .)