The most common and most likely answer to this crossword clue is the 7 plus 4 letter word PRESTER JOHN
I've seen this crossword clue in The Times
P
R
E
S
T
E
R
J
O
H
N
Buddy explains!
The straight part
We know that "Priest-king" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case priest-king = prester john.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.