I just spent a couple of hours trying to understand the UN’s role in the governance of AI. The most important effort seems to be the Global Digital Compact (GDC). An initiative for member states to “outline shared principles for an open, free and secure digital future for all". The GDC has been developed by member states since at least 2021 and will be finalized at the upcoming Summit for the Future in September. Recently, the first draft (Zero Draft) was shared and will be discussed and iterated in the final months before the Summit. The Simon Institute wrote an excellent seven-page response to this. I warmly recommend reading their response but you can find my imperfect summary on the EA Forum.