Native American furious to lose ancestry (5)
I believe the answer is:
incan
'native american' is the definition.
(someone from the Incan Empire)
'furious to lose ancestry' is the wordplay.
'furious' becomes 'incandescent' (incandescent can mean extremely angry).
'to lose' indicates named letters should be taken away.
'ancestry' becomes 'descent' (the ancestors someone is descended from).
'incandescent' with 'descent' removed is 'INCAN'.
(Other definitions for incan that I've seen before include "Of an ancient Andean culture" , "Like some South Americans" , "Of former Peruvian race" , "See old South American" , "Of an ancient civilisation" .)