Next-generation cellular networks will evolve into more complex and virtualized systems, employing machine learning for enhanced optimization and leveraging higher frequency bands and denser deployments to meet varied service demands. This evolution, while bringing numerous advantages, will also pose challenges, especially in mobility management, as it will increase the overall number of handovers due to smaller coverage areas and the higher signal attenuation. To address these challenges, we propose a deep learning based algorithm for predicting the future serving cell utilizing sequential user equipment measurements to minimize the handover failures and interruption time. Our algorithm enables network operators to dynamically adjust handover triggering events or incorporate UAV base stations for enhanced coverage and capacity, optimizing network objectives like load balancing and energy efficiency through transfer learning techniques. Our framework complies with the O-RAN specifications and can be deployed in a Near-Real-Time RAN Intelligent Controller as an xApp leveraging the E2SM-KPM service model. The evaluation results demonstrate that our algorithm achieves a 92% accuracy in predicting future serving cells with high probability. Finally, by utilizing transfer learning, our algorithm significantly reduces the retraining time by 91% and 77% when new handover trigger decisions or UAV base stations are introduced to the network dynamically.