From the very beginning, archers had to protect the volar surface of the forearm that held the bow from being struck
by the bowstring, which could easily sever not unly the skin
but the tendons underneath. I remember seeing pictures of
Assyrian bowmen wearing such a protection, but never saw a
name for them.
The "vambrace" or "rerebrace" was forearm protection, but
apparently not for archers.
Vambrace
(or revebrace). Protection for the lower arms from wrist to elbow, consisting of an upper cannon between the pauldron and cowter, and a lower cannon between the coweter and gauntlet.
Remember the myth about the Amazons, female Greek warriors
who had one breast removed lest the bowstring do it untidily.