The most common and most likely answer to this crossword clue is the 6 letter word KAFTAN
I've seen this crossword clue in The Guardian
K
A
F
T
A
N
More clues leading to the result KAFTAN
Buddy explains!

The straight part
We know that "Eastern garment/Eastern garment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eastern garment/eastern garment = kaftan.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.
What does KAFTAN mean?
KAFTAN noun- A long tunic worn in the Eastern Mediterranean.
- A long dress or shirt similar in style to those worn in the Eastern Mediterranean.