I'm assuming it's already tanned?
If it's tanned, here's what I'd do.... I'd soak it, and once completely rehydrated, I'd wash it really well in a bucket of warm water and Murphy's oil soap. It would bring a nice sheen back to the fur and make it smell better too. Rinse thoroughly afterwards.
If the quiver I wanted to make needed a soft hide, I'd squeeze out the excess water, wait until it was just barely damp, then rub tanning oil into the skin and work it ocassionially as it finished drying. If the quiver needed a stiff hide, I'd stretch it and redry it into the shape I needed.