This paper presents the development of a virtual traffic island-based approach for Urban Airspace Management (UAM) system to resolve simultaneous conflicts. Increasing usage of Unmanned Aerial Vehicle (UAV)-based transportation in urban environments requires a high-density conflict management solution that is both safe and implementable in real time. Existing state-of-the-art methods, including Control Barrier Function (CBF)-based approaches, can guarantee safety, but are not scalable when the number of UAVs is larger. In high-density traffic scenario, the simultaneous existence of multiple conflicts makes real-time execution of conflict resolution a challenging problem. This paper presents a scalable, safe, and implementable dynamic conflict resolution approach called the Virtual Traffic Island (VTI) approach for urban airspace management. The novel VTI approach employs an evolving virtual traffic island with changing radii to handle multiple conflicts simultaneously. In the proposed approach, since each UAV in conflict avoids a single virtual obstacle by solving a CBF-based quadratic programming (QP) problem, the computational requirement for each UAV remains the same, resulting in its easy scalability and safety. The proposed method has been validated for dynamic conflict resolution of a growing number of UAVs in the urban airspace. To validate the implementation aspects of the proposed approach in real time, a software-in-the-loop (SITL) simulation has also been presented. Furthermore, a comparison with other well-known existing methods shows that the novel VTI outperforms these in terms of UAVs reaching their goals and reduces computational complexity, resulting in an easier implementation.