Neat bit turning out to be Asian (7)
I believe the answer is:
tibetan
'be asian' is the definition.
(Tibet is in Asia)
'neat bit turning out' is the wordplay.
'turning out' indicates anagramming the letters.
'neat'+'bit'='neatbit'
'neatbit' is an anagram of 'TIBETAN'.
'to' is the link.
(Other definitions for tibetan that I've seen before include "Former nationality of citizen of Lhasa" , "Oriental" , "Asian" , "mountain man, say" , "Nationality of citizen of Lhasa, before Chinese invasion" .)