H1B Visa, i797 approval and Passport Expiry


New Member
I got my i797 approved( in March 2021) for the position of Professor in CS department in an University in AR, US. Now that the travel ban is in place, my H1B application is refused for the reason I don't fall under the NIE category.
In the meantime, my passport expires in May 2022. Which means I need to travel before Dec 2021 (six months validity of passport). I want to renew my passport now in Sept 2021. My question is, if I get a new passport now and a H1B visa stamped in it, and my i797 approval has the old passport number (one before renewal), will that affect my travel to the US, the job contract etc.?
If yes, pls advice what needs to be done?

Thank you,