A quiver if you have them for use, but not drawn. A rest if it is used to hold the arrow in place during the draw.
If you are talking about the thing that you use to get the arrows out of while you are shooting, then that is called a quiver... If you are talking about the thing that you use to keep your arrows safe, then it is what it sounds like- an arrow case
The archer's Quiver holds the arrows.
A quiver is a container for arrow, bolts and/or darts. The quiver can be attached in different positions on the archers body. There are several different quivers, such as the belt, back, ground and bow quiver that are all worn differently depending on where the archer wants to carry it and they all attach differently. Wikipedia has the different ways a quiver is worn and how to attach it.
A Quiver
Arrows.
in a quiver
the quiver
The 'bag' arrows are carried in is called a quiver.
quiver
The word quiver is the collective noun for a quiver of arrows.
An adjective for the noun quiver could be violent--a violent quiver.
You can just put that barb right back in your quiver.
Quiver
The collective nouns for arrows a 'sheaf of arrows' or a 'quiver of arrows'.
quiver (case for holding arrows)
A group of cobras is called a quiver