The incorporation of Driver Monitoring Systems (DMSs) in vehicles is fundamental to enhancing road safety by continuously assessing driver behavior and identifying signs of fatigue or distraction. However, as these technologies evolve, they also present considerable cybersecurity challenges. This research undertakes an extensive Threat Analysis and Risk Assessment (TARA) of DMSs, adhering to the ISO/SAE 21434 standard, to methodically detect and assess potential security threats. A total of 115 threats were recognized and classified into 95 low-risk, 16 medium-risk, and 4 high-risk scenarios, underscoring key vulnerabilities in data transmission, sensor reliability, and communication frameworks. To mitigate these risks, we suggest a range of countermeasures, including enhanced encryption techniques, stringent authentication protocols, and reinforced access control mechanisms, designed to strengthen the security posture of DMSs in practical applications. This study introduces a structured framework for evaluating and addressing cybersecurity threats in alignment with industry regulations, facilitating the dependable and safeguarded implementation of DMSs in future vehicle architectures while contributing to ongoing progress in automotive cybersecurity.