As agentic AI transitions from general enterprise applications to critical sectors, the definition of risk is transformed, demanding a paradigm shift in security. This chapter provides a deep-dive analysis of deploying autonomous agents in finance, healthcare, and autonomous driving, where the consequences of failure are measured in market stability, human lives, and public safety. It examines sector-specific catastrophic failure modes, including agent-induced flash crashes, adversarial manipulation of medical diagnostics, and the compromise of vehicle perception systems. In response, the chapter details tailored, multi-layered security architectures. Key controls discussed include verifiable circuit breakers for financial trading; non-negotiable human-in-the-loop mandates and privacy-preserving gateways in healthcare; and robust multi-modal sensor fusion for autonomous vehicles. It further illustrates how interoperability standards like the Model Context Protocol (MCP) and Agent-to-Agent (A2A) protocol, when augmented with dedicated security controls, serve as essential architectural patterns for enforcing external governance and auditable collaboration. Ultimately, the chapter argues that earning societal trust for agentic AI in these domains requires a foundational commitment to provably safe, demonstrably robust, and fundamentally trustworthy systems.