Background/Objectives: Aging and chronic stress are regarded as the most important risk factors of cognitive decline. Aged spontaneously hypertensive rats (SHRs) represent a suitable model of age-related vascular brain diseases. The aim of this study was to explore the effects of chronic isolation stress in aging SHRs on their cognitive functions and response to acute stress, as well as the influence of the chronic oral intake of N-Pep-Zn, the Zn derivative of N-PEP-12. Methods: Nine-month-old SHRs were subjected to social isolation for 3 months (SHRiso group), and one group received N-pep-Zn orally (SHRisoP, 1.5 mg/100 g BW). SHRs housed in groups served as the control (SHRsoc). The behavioral study included the following tests: sucrose preference, open field, elevated plus maze, three-chamber sociability and social novelty and spatial learning and memory in a Barnes maze. Levels of corticosterone, glucose and proinflammatory cytokines in blood plasma as well as salivary amylase activity were measured. Restraint (60 min) was used to test acute stress response. Results: Isolation negatively affected the SHRs learning and memory in the Barnes maze, while the treatment of isolated rats with N-Pep-Zn improved their long-term memory and working memory impairments, making the SHRisoP comparable to the SHRsoc group. Acute stress induced a decrease in the relative thymus weight in the SHRiso group (but not SHRsoc), whereas treatment with N-Pep-Zn prevented thymus involution. N-pep-Zn mitigated the increment in blood cortisol and glucose levels induced by acute stress. Conclusions: N-pep-Zn enhanced the adaptive capabilities towards chronic (isolation) and acute (immobilization) stress in aged SHRs and prevented cognitive disturbances induced by chronic isolation, probably affecting the hypothalamo–pituitary–adrenal, sympathetic, and immune systems.