The advancements in computer and networking technologies created closely connected cyberspaces. Nevertheless, this also invalidated many traditional and isolated/local network solutions and introduced higher cybersecurity risk. As a solution, NIST's Zero-Trust Architecture (ZTA) with “never trust, always verify” principle has been widely accepted; yet, its implementation, enforcement, and compliance-check mechanisms are still immature as the solutions are generally applied manually. In this paper, we present an autonomic computing based management engine for networking of a cyberspace, we refer as Autonomic ZTA-based Network Management Engine (AZNME), which monitors an asset's network connections, checks if these connections fulfill ZTA requirements, and evaluates trust continuously, and takes mitigation actions as needed. As a proof of concept, we implemented the AZNME focusing on active connections (e.g., IPs and ports) to enforce policies and create firewall rules based on trust evaluation.