The most common and most likely answer to this crossword clue is the 8 letter word CHEYENNE
I've seen this crossword clue in The Daily Telegraph
C
H
E
Y
E
N
N
E
More clues leading to the result CHEYENNE
- Bashful girl, they say, this Indian
- Indigenous Indian, hence displaced, longing for shelter
- “Coy mistress” said native of Minnesota once
- Former VP endlessly accepts foreign money for Native Americans
- Timid queen said to be associated with 19
- Indian state capital
- Study news written in revolutionary language
- Revolting South American’s desire to touch north-east American native
- Native American evokes retiring Princess
- Indian capital
Buddy explains!

The straight part
We know that "Native American" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case native american = cheyenne.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.