The Sixth Generation (6G) network is a platform for the fusion of the physical and virtual worlds. It will integrate processing, communication, intelligence, sensing, and storage of things. All devices and their virtual counterparts will become part of the service-provisioning process. In essence, 6G is a purposefully cooperative network that heavily depends on the capabilities of edge and end-devices. Digital Twin (DT) will become an essential part of 6G, not only in terms of providing a virtual representation of the physical elements and their dynamics and functionalities but rather DT will become a catalyst in the realization of the cooperative 6G environment. DT will play a main role in realizing the full potential of the 6G network by utilizing the collected data at the cyber twin and then implementing using the physical twin to ensure optimal levels of accuracy and efficiency. With that said, such a cooperative non-conventional network infrastructure cannot rely on conventional centralized intrusion detection and prevention systems. Zero-trust is a new security framework that aims at protecting distributed data, devices, components and users. This article presents a new framework that integrates the zero-trust architecture in DT-enabled 6G networks. Unlike conventional zero-trust solutions, the proposed framework adapts a decentralized mechanism to ensure the security, privacy and authenticity of both the physical devices and their DT counterparts. Blockchain plays an integral part in the authentication of DTs and the communicated data. Artificial Intelligence (AI) is integrated into all cooperating nodes using meta, generalized and federated learning solutions. The article also discusses current solutions and future outlooks, with challenges and some technology enablers.