The aim of the study was to investigate the functional role of the TAAR1 receptor in the formation of the behavioral component of the stress response. The behavior of TAAR1 knockout (TAAR1-KO) mice and wild-type (WT) mice was assessed in anxiety tests—the elevated zero maze (EZM) and novelty-induced hypophagia test (NIHT, hyponeophagia), as well as in the acoustic startle reflex (ASR) test. Testing was performed before and after chronic stress (predator odor/stress model), and also 1.5 months after its cessation to assess long-term behavioral changes. In the EZM test, no significant differences in anxiety levels between TAAR1-KO and WT groups were found either under normal conditions or after stress exposure. However, the stress response dynamics differed between them. In the NSFT, TAAR1-KO mice initially demonstrated motor hyperactivity in response to the novel environment, leading to a sharp decrease in the latency to approach the food, while having no effect on other anxiety scores in this test. Six weeks after the cessation of the stress exposure, anxiety scores continued to increase in mice of both groups. Unlike WT mice, TAAR1-KO mice exhibited specific hyperactivity during the early stages of the EZM and NSFT tests. In the ASR test, there were no intergroup differences before stress. After stress exposure, its impact on the ASR amplitude was more pronounced in TAAR1-KO mice. Conclusions: the TAAR1 receptor plays an important role in modulating the behavioral response to chronic stress, influencing its developmental dynamics and long-term consequences. TAAR1 knockout leads to specific hyperactivity in stressogenic situations and increases the sensitivity of sensorimotor responses to stress.