This chapter explores the integration of Zero Trust Security (ZTS) principles in System-on-Chip (SOC) designs to counter evolving cybersecurity threats. It highlights the limitations of traditional security models and emphasizes the need for continuous authentication, micro-segmentation, and identity verification within SOC architectures. It also deals with Post-Quantum Security (PQS), addressing future cryptographic challenges posed by quantum computing and ensuring long-term protection of embedded systems. Key strategies for implementing ZTS in SOCs include multi-factor authentication (MFA), secure boot, endpoint protection, and encrypted communication, all essential for maintaining robust security. Additionally, the chapter outlines the role of regulatory bodies, compliance standards, and cryptographic algorithms in securing mission-critical applications like automotive, healthcare, and industrial control systems.