Tiny amount shortly consumed by South African once a big drinker (6)
I believe the answer is:
boozer
'a big drinker' is the definition.
'tiny amount shortly consumed by south african once' is the wordplay.
'tiny amount shortly' becomes 'oz' (abbreviation for ounce).
'consumed by' means one lot of letters goes inside another.
'south african once' becomes 'boer'.
'oz' going inside 'boer' is 'BOOZER'.
(Other definitions for boozer that I've seen before include "Pub (sl.)" , "Heavy drinker" , "Inn" , "Pub (slang)" .)