Given Beard's contract has a for-cause firing provision for this exact circumstance, I'd expect to see him fired sooner rather than later.
My best guesses as to who will be the next head coach at Texas are:
Baylor Head Coach Scott Drew
Alabama Head Coach Nate Oats
Iowa State Head Coach T.J Otzelberger
Houston Head Coach Kelvin Sampson
Gonzaga Head Coach Mark Few
Mark Few is at Gonzaga for life, and the same is probably true for Kelvin Sampson and Houston.
I get that Houston would want to make sure he is at Houston for life, but what would be Sampson's motivation? As much as Houston would pour all of their resources in to help him, I have a hard time believing Texas wouldn't spend more for him. Maybe after all the chaos in his career he's happy to just keep doing what is working for him. But that would be pretty stunning if he flatly didn't even consider that move.
I have to admit, this is the first time I have gotten remotely worried about Brad Underwood leaving Illinois. Someone suggested it and I can't get it out of my head. He spent a few years coaching in Texas at SFA. Texas could probably give him incrementally more resources, and perhaps play a little more ball with NIL and admissions than Illinois can. Idk. I'm pretty confident he is pretty happy here, but maybe he thinks he has reached his ceiling. Could be in the realm of Brian Kelly to LSU or Lincoln Riley to USC. You never see it coming, but its not that insane when you really think about it.