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 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 to transmit and reflect the signal from the base station (BS). Firstly, an efficient transmission structure for the ISAC scheme is designed. Then, the time-frequency selective BS-RIS-RSUs channel model are characterized. Based on the estimated cascaded channel parameters (i.e., the delays, the Doppler frequency shifts, the angles of arrivals, and the angles of departure of the scattering paths) of the BS-RIS-RSUs links, the vehicle localization and its velocity can be acquired. With the help of sensing results, the reflection and refraction phase shifts of the STAR-RIS are designed for performance enhancememt. Moreover, the trade-off design for sensing and communication is proposed 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.