The most common and most likely answer to this crossword clue is the 6 letter word MITRED
I've seen this crossword clue in The Daily Telegraph
M
I
T
R
E
D
Buddy explains!

The straight part
We know that "Like prominent cleric" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like prominent cleric = mitred.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 MITRED mean?
MITRED adjective- Relating to an abbot's or bishop's mitre; wearing a mitre.
- Having a mitre joint.