The most common and most likely answer to this crossword clue is the 5 letter word COTTA
C
O
T
T
A
Buddy explains!

The straight part
We know that "Short vestment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case short vestment = cotta.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 COTTA mean?
COTTA noun- A surplice, in England and America usually one shorter and less full than the ordinary surplice and with short sleeves, or sometimes none.
- A kind of coarse woollen blanket.