The most common and most likely answer to this crossword clue is the 9 letter word KATHAKALI
I've seen this crossword clue in The Guardian
K
A
T
H
A
K
A
L
I
More clues leading to the result KATHAKALI
Buddy explains!

The straight part
We know that "Indian dance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case indian dance = kathakali.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 KATHAKALI mean?
KATHAKALI noun- A spectacular lyric dance drama of southern India performed with acrobatic energy and highly stylized pantomime.