The most common and most likely answer to this crossword clue is the 8 letter word CASSOCKS
I've seen this crossword clue in The Daily Telegraph
C
A
S
S
O
C
K
S
Buddy explains!

The straight part
We know that "Vestments" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vestments = cassocks.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 CASSOCKS mean?
CASSOCKS noun- A military cloak or long coat worn by soldiers or horsemen in the 16th and 17th centuries.
- A coarse, loose cloak or gown, worn by women, sailors, shepherds, countryfolk etc.
- An item of clerical clothing: a long, sheath-like, close-fitting, ankle-length robe worn by clergy members of some Christian denominations.