It is somewhat unclear how much Uranium is available worldwide (for strategic reasons), but even at current production, supply issues have been known to happen.
Nuclear fission using Uranium is not sustainable. If we expand current nuclear technologies to tackle climate change then we’d likely run out of Uranium by 2100. Nuclear fusion using Thorium might be sustainable, but it’s not yet a proven, scalable technology. And all of this is ignoring the long lead times, high costs, regulatory hurdles and nuclear weapon proliferation concerns that nuclear typically presents. It’d be great if nuclear was the magic bullet for climate change, but it just ain’t.