Consumers seeking a new mobile plan have many choices in the present mobile landscape. The Mobile Virtual Network Operator (MVNO) has recently gained considerable attention among these options. MVNOs offer various benefits, making them an appealing choice for a majority of consumers. These advantages encompass flexibility, access to cutting-edge technologies, enhanced coverage, superior customer service, and substantial cost savings. Even though MVNO offers several advantages, it also creates some security and privacy concerns for the customer simultaneously. For instance, in the existing solution, MVNO needs to hand over all the sensitive details, including the users' identities and master secret keys of their customers, to a mobile operator (MNO) to validate the customers while offering any services. This allows MNOs to have unrestricted access to the MVNO subscribers' location and mobile data, including voice calls, SMS, and Internet, which the MNOs frequently sell to third parties (e.g., advertisement companies and surveillance agencies) for more profit. Although critical for mass users, such privacy loss has been historically ignored due to the lack of practical and privacy-preserving solutions for registration and handover procedures in cellular networks. In this paper, we propose a universally composable authentication and handover scheme with strong user privacy support, where each MVNO user can validate a mobile operator (MNO) and vice-versa without compromising user anonymity and unlinkability support. Here, we anticipate that our proposed solution will most likely be deployed by the MVNO(s) to ensure enhanced privacy support to their customer(s).