The most common and most likely answer to this crossword clue is the 6 letter word BODICE
I've seen this crossword clue in Financial Times
B
O
D
I
C
E
More clues leading to the result BODICE
- Flesh mostly to freeze in tight corset
- Top bloke has reserve
- Bishop spotted cubes on old garment
- . Old British queen ignoring articles, 2?
- Old bones alongside black garment
- . Person with diamonds in upper part of dress
- Chap with cool top
- How could I be Doc?
- Old things spotted under black vest
- Only a couple of bookies gamble — may this have restricted the figure?
Buddy explains!

The straight part
We know that "vest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vest = bodice.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 BODICE mean?
BODICE noun- A sleeveless shirt for women, sometimes provided with detachable sleeves.
- Blouse; any shirt for women, particularly the upper part of a two-piece dress or European folk costume.
- The upper portion of a women's one-piece dress, equivalent to a shirt.
- Underbodice: an undershirt for women, particularly a corset or other undershirt stiffened with whalebone.