Mother right — drink makes difference! (6)
I believe the answer is:
margin
'difference' is the definition.
(margin is a kind of difference)
'mother right drink' is the wordplay.
'mother' becomes 'ma' (Ma is another word for mother or mum).
'right' becomes 'r' (common abbreviation).
'drink' becomes 'gin' (gin is a kind of drink).
'ma'+'r'+'gin'='MARGIN'
'makes' is the link.
(Other definitions for margin that I've seen before include "Permissible difference" , "Periphery" , "Edge, border, fringe" , "bank" , "Blank space around a text" .)