This paper introduces MEDIATE, a framework that brings zero trust principles to the Cloud-Edge-IoT Computing Continuum. MEDIATE integrates several software-based security and policy services operating at the cloud and edge layers with hardware- and software-based monitoring components as IoT devices deployed close to the assets that require security protection. The framework is designed to a three-layer architecture with Orchestrator (Cloud), Overwatch (Edge), and Sentinel (IoT) that collectively enables cross-layer policy enforcement and coordinated threat mitigation. The Orchestrator provides global view and policy consistency, the Overwatch performs local analysis and threat correlation, and the Sentinel acts as a lightweight agent for real-time monitoring near critical assets. These components provide an adaptive security foundation suitable for distributed and large-scale operational domains such as Fourth-Party Logistics (4PL).