The most common and most likely answer to this crossword clue is the 4 letter word HADJ
I've seen this crossword clue in Independent
H
A
D
J
More clues leading to the result HADJ
- One pillar contained top of joist
- Spiritual trip experienced on joints primarily
- Henry joins Bill and Jack for trip to Mecca
- Religious duty enjoyed by justice
- Spiritual journey made by Juliet in the wake of husband Bill
- Spiritual journey Jack experienced when swapping sides
- Spiritual trip experienced by junkie primarily
- For starters, have a diphtheria jab for Saudi trip
- Pilgrim’s journey Jack’s done first
- Pilgrimage had a desert journey, for starters
Buddy explains!

The straight part
We know that "Religious duty (for Muslims)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case religious duty (for muslims) = hadj.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 HADJ mean?
HADJ noun- The pilgrimage to Mecca made by pious Muslims; one of the five pillars of Islam.