The rules that already apply to your industry, which do not stop applying because a model is involved. Financial services, healthcare, employment, education and law all have existing regimes covering fairness, record-keeping, professional responsibility and evidence, and those are usually more immediately binding than any AI-specific law.
Technical view
Examples include model risk management expectations in banking, medical device regulation where software has a diagnostic or therapeutic purpose, employment law on discrimination in recruitment tools, and professional conduct rules requiring competent supervision of work product. Sector regulators generally take the position that existing rules apply unchanged, which means the first compliance question is not what AI law says but what your regulator already requires.
Related
Part of AI Terminology Index, section: Governance, Law and Regulation.