In this paper, we investigate an Unmanned Aerial Vehicle (UAV)-enabled integrated sensing and communications scenario, where the UAV simultaneously serves terrestrial communication users and detects terrestrial sensing targets. Traditional subcarrier allocation schemes, such as fully-overlapped or non-overlapped designs, suffer from mutual interference or inefficient spectrum utilization. To address this issue, we propose a Partially-Overlapped (PO) subcarrier allocation scheme that dedicates a fraction of subcarriers for sensing, while supporting communication across the full bandwidth. Based on the PO-based subcarrier allocation scheme, an integrated optimization problem is formulated to jointly design the beamforming, subcarrier allocation, and UAV trajectory, with the objective of maximizing the weighted throughput under sensing constraints. By applying Lyapunov optimization, the original problem is reformulated into a time-slotted drift-plus-penalty problem. To solve the non-convexity, it is decoupled into three subproblems: beam-forming design, subcarrier allocation, and UAV trajectory design, which are iteratively solved by utilizing an alternating optimization framework. Through numerical results, we demonstrate that the proposed algorithm outperforms baseline schemes (i.e., the fully-overlapped scheme and the non-overlapped scheme). Furthermore, it achieves a favorable balance between the communication throughput and sensing performance by judiciously adjusting Lyapunov control parameter.