Integrated sensing and communication (ISAC) has become an attractive technology for future wireless networks. In this paper, we propose a simultaneous transmission and reflection reconfigurable intelligent surface (STAR-RIS) aided dynamic scatterers tracking scheme for ISAC in high mobility millimeter wave communication systems, where the STAR-RIS is employed to provide communication service for indoor user with the base station (BS) and simultaneously sense and track the interested outdoor dynamic scatterers. Specifically, we resort to an active STAR-RIS to respectively receive and further deal with the impinging signal from its double sides at the same time. Then, we develop a transmission strategy with the activation scheme of the STAR-RIS elements, and construct the signal models within the system. After acquiring the channel parameters related to the BS-RIS channel, the dynamic paths can be identified from all the scattering paths, and the dynamic targets can be classified with respect to their radar cross sections. We further track the outdoor scatterers at STAR-RIS by resorting to the Gaussian mixture-probability hypothesis density filter. With the tracked locations of the outdoor scatterers, a beam prediction strategy for both the precoder of BS and the refraction phase shift vector of STAR-RIS is developed to enhance the communication performance of the indoor user. Besides, a target mismatch detection and path collision prediction mechanism is proposed to reduce the training overhead and improve the transmission performance. Finally, the feasibility and effectiveness of our proposed STAR-RIS aided dynamic scatterers tracking scheme for ISAC are demonstrated and verified via simulation results.