Integrated sensing and communication (ISAC) has become a promising technology for future communication system. In this paper, we consider a millimeter wave system over high mobility scenario, and propose a novel simultaneous transmission and reflection reconfigurable intelligent surface (STAR-RIS) aided ISAC scheme. To improve the communication service of the in-vehicle user equipment (UE) and simultaneously track and sense the vehicle with the help of nearby roadside units (RSUs), a STAR-RIS is equipped on the outside surface of the vehicle. Firstly, an efficient transmission structure is developed, where a number of training sequences with orthogonal precoders and combiners are respectively utilized at BS and RSUs for channel parameter extraction. Then, the near-field static channel model between the STAR-RIS and in-vehicle UE as well as the far-field time-frequency selective BS-RIS-RSUs channel model are characterized. By utilizing the multidimensional orthogonal matching pursuit (MOMP) algorithm, the cascaded channel parameters of the BS-RIS-RSUs links can be obtained at the RSUs. Thus, the vehicle localization and its velocity measurement can be acquired by jointly utilizing these extracted cascaded channel parameters of all RSUs. Note that the MOMP algorithm can be further utilized to extract the channel parameters of the BS-RIS-UE link for communication. With the help of sensing results, the phase shifts of the STAR-RIS are delicately designed, which can significantly improve the received signal strength for both the RSUs and the in-vehicle UE, and can finally enhance the sensing and communication performance. Moreover, the trade-off for sensing and communication is designed by optimizing the energy splitting factors of the STAR-RIS. Finally, simulation results are provided to validate the feasibility and effectiveness of our proposed STAR-RIS aided ISAC scheme.