The most common and most likely answer to this crossword clue is the 6 letter word CALIPH
I've seen this crossword clue in The Daily Telegraph
C
A
L
I
P
H
More clues leading to the result CALIPH
- Religious leader shows a brashness in church
- A kiss in church for religious leader
- Sultan‘s companion consuming a sauce
- … check arresting a border leader
- Cut tail parts off pilchard to be cooked for Islamic leader
- Religious leader given a kiss in church
- Leader is tricky chap, predominantly ill disposed at heart
- Spiritual leader lacking energy in chapel I roused
- Religious leader — his name perhaps has power in church
- Old spiritual leader caught boxer by pub
Buddy explains!

The straight part
We know that "Islamic leader" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case islamic leader = caliph.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 CALIPH mean?
CALIPH noun- The political leader of the Muslim world, successor of Muhammad's political authority, not religious or spiritual.