Background: The scientific literature on COVID-19 and its long-term impacts on all-body systems and their treatments is still limited. The aim of the study was to create a safe protocol-based intervention to improve functional and equilibrium abilities in older adults impacted by COVID-19. Methods: This study used a sample of 46 people (intervention group: n = 26; control group: n = 20). Resistance training (RT) was held twice a week, with 60 min per session for 8 weeks. The postural stability and quality of life questionnaire (WHQOOL) was completed during pre- and post-testing. Results: The results indicated significant differences in overall stability index (OSI) with eyes open (EO), anterior–posterior stability index (APSI) EO, fall-risk index 6-2 (FRI6-2) values in males (p < 0.05), and APSI EO (p < 0.05) values in females compared to control groups, respectively. In the training, a significant improvement was reported in OSI EO and APSI EO (p < 0.05) female groups compared to baseline results and in FRI6-2 values in both gender groups (p < 0.01—men, p < 0.05—women). The effect of the intervention was recorded in the intervention group in the OSI EO (Z = −3.12, p < 0.01, R = 0.533) and FRI6-2 (Z = −2.06, p < 0.05, R = 0.354). Additionally, significantly different reactions between the groups were observed in the psychological domain (DOM2) (Z = 2.194, p < 0.028, R = 0.389), social relationship domain (DOM3) (Z = 2.051, p < 0.0403, R = 0.361), and in question 2 concerning general health (Z = 3.309, p < 0.0009, R = 0.535). Conclusions: The findings indicate that RT had a positive effect on older adults affected by COVID-19, led to a significant improvement in their postural stability, and had a significant impact on elements of psychological well-being and quality of life.