The aim of our study was to examine the position of vaccinated people regarding the proposal for mandatory and seasonal vaccination against COVID-19 in Serbia. A cross-sectional study was conducted in a sample of people who came to receive a third dose of COVID-19 at the Institute of Public Health of Serbia in September and October 2021. Data were collected by means of a sociodemographic questionnaire. The study sample comprised 366 vaccinated adults. Factors associated with the belief that vaccination against COVID-19 should become mandatory were being married, being informed about COVID-19 from TV programmes and medical journals, trust in health professionals, and having friends affected by COVID-19. In addition to these predictors, factors associated with the belief that COVID-19 vaccination should become seasonal were being older, consistently wearing facemasks, and not being employed. The results of this study highlight that trust in information delivery, evidence-based data, and healthcare providers may be a major driver of mandatory and seasonal vaccine uptake. A careful assessment of the epidemiological situation, the capacity of the health system, and the risk–benefit ratio is needed in order to introduce seasonal and/or mandatory vaccination against COVID-19.