The most common and most likely answer to this crossword clue is the 4 letter word SHIA
S
H
I
A
More clues leading to the result SHIA
- Branch of religion has diversified round Italy
- Ismailian, he: ‘I am involved with – line’ maybe?
- One has converted to branch of Islam
- Muslim girl given a voice
- Branch of religion found in southern Haifa, oddly
- Old ruler of Iran largely accepts single branch of Islam
- Primarily, someone honouring ‘Infallible Ali’?
- Primarily, someone honouring 'Infallible Ali'?
Buddy explains!

The straight part
We know that "Primarily, someone honouring ‘Infallible Ali’" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case primarily, someone honouring ‘infallible ali’ = shia.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.