though I think just "gauntlet" may be as good a term

I was going to put "cuff extension" first, though that seemed for work gloves, e.g. for welding

Gauntlet Cuff

A glove cuff designed for extra protection for the forearm. Usually a 4½ " cuff. Slides on and off easily and allows for maximum movement of forearm.

http://www.fitslikeaglove.org/01_Site/articles/art_GloveTerm...

The gauntlet is that part of the glove below the wrist, and nowadays it is usually cut in one with the rest of the trank. It probably dates back to the time when men wore coats of mail and gloves were worn under the steel gauntlet to prevent chafing. It served to cover the end of the sleeve and enabled the glove to be pulled on easily. Nowadays the gauntlet has ceased to be an important part of the glove and is almost non-existent. In former times it was often elaborately embroidered and extended halfway up the forearm. Some gloves, of course, still have deep gauntlets, particularly those worn by motorcyclists.
http://www.kingsmerecrafts.com/page88.html