The most common and most likely answer to this crossword clue is the 10 letter word ARCHBISHOP
I've seen this crossword clue in Independent
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More clues leading to the result ARCHBISHOP
- Cleric — a Roman Catholic — bound to admit mistake
- See controller teasing man on board
- Mischievous piece on man of the cloth
- Senior cleric, shrewd man
- Cunning black rat traps one primate
- See boss teasing man on board
- Pibroch has upset primate
- Church high-up‘s cold, seeking accommodation in parish with hob for cooking
- See leader’s husband introduced to chap Boris sacked
- See manager using spanner, note, prior to current workplace
Buddy explains!

The straight part
We know that "primate" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case primate = archbishop.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 ARCHBISHOP mean?
ARCHBISHOP noun- A senior bishop who is in charge of an archdiocese, and presides over a group of dioceses called a province (in Catholicism, Eastern Orthodoxy, Anglicanism, etc.)