The most common and most likely answer to this crossword clue is the 7 letter word BIRETTA
I've seen this crossword clue in The Times
B
I
R
E
T
T
A
More clues leading to the result BIRETTA
- What could be held up by hatter, I bet
- Retired hatter, I believe, can stock priest's headgear
- Attire prepared to be put on bishop
- Attire worn by bishop?
- Some matter I brought up that covers a Catholic priest
- Cap fantastic bit-rate
- Bishop has one on extremely tight, a square cap
- Chance to get hold of Irish teaching assistant — it goes to father’s head
- Stiff cap tailored treat, bishop has one on
- Bishop’s attire, possibly
Buddy explains!

The straight part
We know that "Attire worn by bishop" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case attire worn by bishop = biretta.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 BIRETTA mean?
BIRETTA noun- A square cap, originally with four ridges across the top, surmounted by a tuft, worn by Roman Catholic clergy (and by some in the Anglican Church). A three-sided biretta is worn by Roman Catholic clergy for liturgical celebrations.