Hypertension is one of the most significant risk factors for many cardiovascular diseases. At different stages of hypertension development, various pathophysiological processes can play a key role in the manifestation of the hypertensive phenotype and of comorbid conditions. Accordingly, it is thought that when diagnosing and choosing a strategy for treating hypertension, it is necessary to take into account age, the stage of disorder development, comorbidities, and effects of emotional–psychosocial factors. Nonetheless, such an approach to choosing a treatment strategy is hampered by incomplete knowledge about details of age-related associations between the numerous features that may contribute to the manifestation of the hypertensive phenotype. Here, we used two groups of male F2(ISIAHxWAG) hybrids of different ages, obtained by crossing hypertensive ISIAH rats (simulating stress-sensitive arterial hypertension) and normotensive WAG rats. By principal component analysis, the relationships among 21 morphological, physiological, and behavioral traits were examined. It was shown that the development of stress-sensitive hypertension in ISIAH rats is accompanied not only by an age-dependent (FDR < 5%) persistent increase in basal blood pressure but also by a decrease in the response to stress and by an increase in anxiety. The plasma corticosterone concentration at rest and its increase during short-term restraint stress in a group of young rats did not have a straightforward relationship with the other analyzed traits. Nonetheless, in older animals, such associations were found. Thus, the study revealed age-dependent relationships between the key features that determine hypertension manifestation in ISIAH rats. Our results may be useful for designing therapeutic strategies against stress-sensitive hypertension, taking into account the patients’ age.