The most common and most likely answer to this crossword clue is the 3 plus 7 letter word EID AL-FITR
I've seen this crossword clue in The Guardian
E
I
D
A
L
-
F
I
T
R
Buddy explains!
The straight part
We know that "Muslim festival" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case muslim festival = eid al-fitr.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.