Cloud-native computing enhances the deployment of microservice architecture (MSA) applications by improving scalability and resilience, particularly in Beyond 5G (B5G) environments such as Sixth-Generation (6G) networks. This is achieved through the ability to replace traditional hardware dependencies with software-defined solutions. While service meshes enable secure communication for deployed MSAs, they struggle to identify vulnerabilities inherent to microservices. The reliance on third-party libraries and modules, essential for MSAs, introduces significant supply chain security risks. Implementing a zero-trust approach for MSAs requires robust mechanisms to continuously verify and monitor the software supply chain of deployed microservices. However, existing service mesh solutions lack runtime trust evaluation capabilities for continuous vulnerability assessment of third-party libraries and modules. This paper introduces a mechanism for continuous runtime trust evaluation of microservices, integrating vulnerability assessments within a service mesh to enhance the deployed MSA application. The proposed approach dynamically assigns trust scores to deployed microservices, rewarding secure practices such as timely vulnerability patching. It also enables the sharing of assessment results, enhancing mitigation strategies across the deployed MSA application. The mechanism is evaluated using the Train Ticket MSA, a complex open-source benchmark MSA application deployed with Docker containers, orchestrated using Kubernetes, and integrated with the Istio service mesh. Results demonstrate that the enhanced service mesh effectively supports dynamic trust evaluation based on the vulnerability posture of deployed microservices, significantly improving MSA security and paving the way for future self-adaptive solutions.