Waistcoat

sleeveless garment for the upper body, usually worn over a shirt and below a coat; it covers the back, shoulders and bust

A waistcoat (known as a vest in the United States) is a sleeveless upper-body garment. It is worn over a dress shirt and necktie, and below a coat as a part of most men's formal wear. It is the third piece of the three-piece male suit.[1]

A traditional waistcoat, to be worn with a two-piece suit or separate jacket and trousers.
French waistcoat in silk, circa 1750, LACMA.

References

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  1. Gavenas, Mary Lisa (2008). Encyclopedia of Menswear. New York: Fairchild. p. 379. ISBN 978-1-56367-465-5.
 
Man's court coat and waistcoat, 1800