The most common and most likely answer to this crossword clue is the 8 letter word NINJUTSU
I've seen this crossword clue in The Guardian
N
I
N
J
U
T
S
U
Buddy explains!

The straight part
We know that "Asian art" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case asian art = ninjutsu.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 NINJUTSU mean?
NINJUTSU noun- A Japanese martial art that is a collection of techniques originally practiced for Japanese espionage purposes, and includes methods of gathering information, nondetection, avoidance, and misdirection techniques. Used by ninja (忍者).