The COVID-19 pandemic has had a detrimental effect on the global economy, including the insurance industry. It has forced financial markets to confront a new risk directly related to the virus’s rapid spread. Therefore, the paper aims to determine possible risks or opportunities that insurance companies may encounter, considering both pre- and post-pandemic phases. For this purpose, financial data of 110 Romanian insurance companies for 2016–2022 were analyzed. The topfirme platform was used in the data collection process. Subsequently, based on statistical analysis methods, an econometric model was developed to evaluate the turnover for insurance companies in Romania. When developing the model equation, establishing dependent and independent variables based on the Altman model or the Z-model of bankruptcy prediction was considered. Thus, the findings indicate that employees are the primary factor in these businesses’ proper operation and increased profitability. It is emphasized that turnover directly depends on these variables since the number of employees is a variable around which incomes and expenses fluctuate. Turnover is affected positively or negatively depending on employee productivity and workload, which can lead to increased revenues and decreased costs, or vice versa. Accordingly, an insurance company’s HR department should resolve issues that crop up during the shift to telemedicine, enhance workers’ digital skills, provide them with moral and psychological support, and foster stable working relationships. It should also implement strategies to sustain and raise employee engagement levels, fortify control measures, and alter internal communications.