The adoption of hybrid cloud architectures has accelerated across enterprises seeking to balance scalability, cost efficiency, and regulatory compliance, particularly as data intensive applications increasingly span on premises infrastructure and public cloud services, creating tightly coupled yet operationally fragmented execution environments. Databases and Big Data platforms operating across these heterogeneous domains introduce compounded security, governance, and compliance challenges that extend beyond traditional perimeter models, including fractured trust boundaries, non-uniform identity propagation, divergent encryption postures, complex data residency and sovereignty constraints, and reduced end to end auditability across distributed storage and processing layers. This article synthesizes established security frameworks, regulatory standards, and foundational academic research to articulate a structured, end to end security posture for hybrid cloud database environments, integrating architectural guidance from the NIST Cloud Computing Reference Architecture with cryptographic enforcement models derived from encrypted query processing systems such as CryptDB and operational best practices observed in production grade distributed databases including MongoDB, Apache Cassandra, and DataStax Enterprise. The proposed layered security and compliance framework aligns data plane protections, control plane governance, and operational monitoring through coordinated application of field level and transport encryption, federated identity and policy based access control, continuous telemetry driven auditing, and formalized control mapping to regulatory requirements, demonstrating how enterprises can preserve confidentiality, enforce compliance, and sustain fault tolerant, high throughput Big Data operations across cloud boundaries without compromising scalability or performance.