The Nevada DMV has an official extension to September 13 per
https://dmvnv.com/index.htm, so technically and legally your license expiration date is now 9/13. I would print the official extension letter from the site and keep it with your DL, and change the expiration date in your Fastbreak account if you have one. There are other situations (at least on California) where an older photo-id card is combined with a paper license while waiting for a card to be delivered, for example.
If renting in NV the agents are likely already aware. Elsewhere be prepared to show the letter (but I might not unless the agent notices, because why even create a question in their mind if they don't). Nothing is guaranteed, but you want to be certain of yourself and use the right terminology ("No, my license expiration is not until 9/13, as this letter states and you can verify on the NV DMV site")