The most common and most likely answer to this crossword clue is the 4 letter word HAJJ
I've seen this crossword clue in The Guardian
H
A
J
J
Buddy explains!

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 HAJJ mean?
HAJJ noun- The pilgrimage to Mecca made by pious Muslims; one of the five pillars of Islam.