Get drinkers' club to welcome non-drinker in (6)
I believe the answer is:
attain
'get' is the definition.
(attaining is a kind of getting)
'drinkers' club to welcome non-drinker in' is the wordplay.
'drinkers' club' becomes 'AA' (Alcoholics Anonymous).
'to welcome' is an insertion indicator (in sense of 'inviting in').
'non drinker' becomes 'tt' (Teetotaller abbreviation).
'aa' going around 'tt' is 'atta'.
'atta'+'in'='ATTAIN'
(Other definitions for attain that I've seen before include "Arrive at or achieve" , "Succeed in reaching, achieve" , "Arrive at, accomplish" , "Reach or gain" , "Succeed in doing, get there" .)