Integrated sensing and communication (ISAC) has emerged as a promising key technology for future wireless networks, enabling the efficient coordination of sensing and communication functions within limited resources. This work investigates a secure ISAC system assisted by an uncrewed aerial vehicle (UAV). By incorporating the extended Kalman filter (EKF), the proposed system is capable of delivering communication services to legitimate users while simultaneously jamming eavesdroppers and performing joint prediction and tracking of the trajectories of both legitimate and illegitimate users. Considering practical constraints such as {sensing beamwidth}, transmit power, and UAV's propulsion energy consumption, the secrecy rate is maximized through the joint design of transmit beamforming and UAV trajectory. To tackle the resulting highly non-convex optimization problem, an efficient iterative algorithm is developed by integrating block coordinate descent, successive convex approximation, and EKF, thereby yielding a high-quality suboptimal solution. Extensive simulation results validate the superior performance of the proposed scheme compared to benchmarks.