Native American's refusal to drink coffee from the south (6)
I believe the answer is:
navajo
'native american's' is the definition.
(I've seen this before)
'refusal to drink coffee from the south' is the wordplay.
'refusal' becomes 'no'.
'to drink' is an insertion indicator.
'coffee' becomes 'java' (synonyms).
'from the south' is a reversal indicator (in a down clue, letters go up).
'java' back-to-front is 'avaj'.
'no' going around 'avaj' is 'NAVAJO'.
(Other definitions for navajo that I've seen before include "Native American from Arizona, New Mexico or Utah" , "US native language" , "N American Indian tribe" , "Native American - on Java (anag)" , "A N. American Indian people" .)