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Accurate and efficient ship tracking by geosynchronous orbit (GEO) satellites holds great significance for large-scale maritime surveillance. Nevertheless, ship tracking continues to grapple with a multitude of challenges as follows: 1) the targets are small and often obscured by cloud interference, leading to weakened features; 2) the contrasts between the ships and the background are relatively low, complicating the identification and tracking process; and 3) the frame-to-frame relative positioning accuracy is poor, posing difficulties in reflecting the actual movement trends of ships. In response to these challenges, we proposed TS-Track, a novel framework employing multilevel supervision paradigm to improve tracking performance. Initially, this framework restructured the tracking task into three key sub-modules: image enhancement, object tracking, and trajectory adjustment, inherently fostering a unified training protocol that naturally encompasses all components. Subsequently, a trajectory-based frame fusion strategy was proposed, utilizing consecutive three-frame images to enhance target features and produce consistent motion feature patterns; Last but not least, a trajectory adjustment network was developed to correct the position of ships during tracking, resulting in stable tracking trajectories, and reproduce the actual movement trends of ships. The experimental results on GaoFen-4 dataset validated that our method delivered a significant improvement in ship tracking and achieved state-of-the-art (SOTA) performance. Source codes are available at https://github.com/KTqizhi/KTqizhi.github.io.