Hybrid cloud computing has become an essential technological approach for large-scale enterprise computing systems due to its ability to combine the flexibility of public cloud services with the control and security of private cloud infrastructures. As organizations increasingly migrate critical workloads and sensitive data to hybrid environments, ensuring security, privacy, and regulatory compliance has become a major challenge. This study explores hybrid cloud security and compliance frameworks designed to protect enterprise computing systems from cyber threats, unauthorized access, data breaches, and operational vulnerabilities. The research examines the architectural components, security mechanisms, governance models, and compliance strategies implemented within hybrid cloud infrastructures. Technologies such as encryption, identity and access management, intrusion detection systems, multi-factor authentication, and security information and event management are analyzed in the context of enterprise cloud security. The study also evaluates compliance frameworks including GDPR, HIPAA, ISO 27001, and PCI-DSS that guide organizations in maintaining regulatory standards. Findings indicate that hybrid cloud frameworks provide improved scalability, operational flexibility, disaster recovery, and cost efficiency while supporting secure enterprise computing operations. However, challenges related to interoperability, policy enforcement, data governance, and complex infrastructure management remain significant concerns. The study concludes that effective hybrid cloud security and compliance frameworks are critical for sustainable and secure enterprise digital transformation.