The increasing adoption of artificial intelligence (AI), cloud infrastructure, large language models, automation, and distributed computing is transforming government information systems while simultaneously expanding their cybersecurity, privacy, and governance risks. Public-sector AI systems process sensitive information, operate across heterogeneous infrastructures, and increasingly support decisions with direct consequences for citizens. This paper develops a privacy-preserving AI governance framework for government systems by integrating cybersecurity governance, responsible AI principles, infrastructure automation, cloud security, self-healing capabilities, and explainability. The study adopts a structured conceptual research methodology based exclusively on the supplied literature and synthesizes its implications for public-sector innovation. The proposed framework consists of six interconnected layers: governance and accountability, privacy protection, cybersecurity controls, secure infrastructure orchestration, explainable AI assurance, and continuous monitoring and self-healing. The analysis indicates that privacy and cybersecurity should not be treated as independent compliance activities; instead, they should be embedded throughout the AI system lifecycle and infrastructure-management process. The framework further emphasizes policy enforcement, configuration integrity, transparent decision processes, automated recovery, and human oversight. Findings suggest that automation can improve resilience and operational consistency, but excessive autonomy may introduce new governance risks when systems modify infrastructure or decisions without adequate authorization. The paper therefore proposes a balanced governance model in which AI-enabled automation is constrained by explicit policies, auditability, privacy controls, and human accountability. The resulting framework provides a conceptual foundation for secure and responsible public-sector AI innovation while identifying limitations associated with heterogeneous environments, evolving threats, and the need for empirical validation.