Integrated Sensing and Communication (ISAC) has emerged as a promising solution in addressing the challenges of high-mobility scenarios in 5G NR Vehicle-to-Infrastructure (V2I) communications. This paper proposes a novel sensing-assisted handover framework that leverages ISAC capabilities to enable precise beamforming and proactive handover decisions. Two sensing-enabled handover triggering algorithms are developed: a distance-based scheme that utilizes estimated spatial positioning, and a probability-based approach that predicts vehicle maneuvers using interacting multiple model extended Kalman filter (IMM-EKF) tracking. The proposed methods eliminate the need for uplink feedback and beam sweeping, thus significantly reducing signaling overhead and handover interruption time. A sensing-assisted NR frame structure and corresponding protocol design are also introduced to support rapid synchronization and access under vehicular mobility. Extensive link-level simulations using real-world map data demonstrate that the proposed framework reduces the average handover interruption time by over 50%, achieves lower handover rates, and enhances overall communication performance.