The most common and most likely answer to this crossword clue is the 6 letter word EXARCH
I've seen this crossword clue in Independent
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Buddy explains!
The straight part
We know that "bishop" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bishop = exarch.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 EXARCH mean?
EXARCH noun- In the Byzantine Empire, a governor of a distant province.
- In the Eastern Christian Churches, the deputy of a patriarch, or a bishop who holds authority over other bishops without being a patriarch.
- In these same churches, a bishop appointed over a group of the faithful not yet large enough or organized enough to constitute an eparchy or diocese.