Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS), which consists of numerous passive elements, has recently emerged in wireless communication systems as a promising technology providing 360$^\circ$ coverage and better performance. In our research, we introduce an active STAR-RIS (ASTARS)-aided integrated sensing and communications (ISAC) system designed to optimize the radar signal-to-noise ratio (SNR), enhancing detection and signal transmission efficiency. The introduction of an ISAC system aims to improve both communication efficiency and sensing capabilities. Also, we employ orthogonal frequency division multiplexing (OFDM) to address the frequency-selective fading problem. Furthermore, we evaluate the radar sensing capabilities by examining the range and velocity, and assess the performance through the mean-squared error (MSE) of their estimations. Our simulation results demonstrate that ASTARS outperforms STAR-RIS in our system configurations, and that the proposed optimization approach further enhances the system performance. Additionally, we confirm that an increase in the subcarrier spacing can reduce the transmission bit error rate (BER) under high-velocity conditions.