Sleeve garter

It came into wide use especially in the United States in the latter half of the 19th century, when men's ready-made shirts came in a single (extra long) sleeve length.

While this is widely understood to make it more difficult for the dealer to cheat by concealing a card in his sleeve, the sleeve garter is usually accompanied by a vest and bow tie (and sometimes a visor), suggesting this usage might date to late 19th and early 20th-century fashion as much as it serves a real purpose.

In this case, the suggestion may be that the sleeve garter facilitates freedom of movement and aids in gunslingers’ ability to quick draw.

A small ornamental plate called a “concho”, typically with an Old West motif, may be attached to the garter.

[4] Day Dreaming Bookkeeper, Norman Rockwell's 1924 illustration, shows an accountant wearing a vest, a visor, a bow tie and very narrow sleeve garters.