I just looked at my app. I'm not aware of any way to rent from Audible. If you have the Premium Plus membership, you get one credit per month, plus you can access the "Plus Catalog" for free-to-listen content. With the credit, you can buy audiobooks that you will own. I think the free-to-listen is only accessible for as long as you have the membership, but I'm not 100% sure bc I still have it.

If you have Overdrive/Libby, you can borrow from your local library.