The most common and most likely answer to this crossword clue is the 6 plus 3 plus 6 letter word SINBAD THE SAILOR
I've seen this crossword clue in The Guardian
S
I
N
B
A
D
T
H
E
S
A
I
L
O
R
More clues leading to the result SINBAD THE SAILOR
Buddy explains!

The straight part
We know that "of the Arabian Nights" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case of the arabian nights = sinbad the sailor.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.