In this study, a dynamic mixture copula is used to estimate the marginal expected shortfall in the South African insurance sector. While other studies assumed nonlinear dependence to be static over time, our model capture time-varying nonlinear dependence between institutions and the market. In order to capture time-varying nonlinear dependence, the generalized autoregressive score (GAS) is used to model the dynamic copula parameters. Furthermore, our study implements a ranking that expresses to what degree individual insurers are systemically important in South Africa. We use daily stock return of five South African insurers listed in the Johannesburg Stock Exchange (JSE) from November 13, 2007 to June 15, 2020. We find that Sanlam and Discovery contribute the most to systemic risk, while Santam is found to be the least contributor to the overall systemic risk in the South African insurance sector. Our findings would be of paramount importance for the South African regulators as they would be informed that not only banks are systemically important, but some insurers also are systemically important financial institutions. Hence, stricter regulation of these institutions in the form of higher capital and loss absorbency requirements could be required based on the individual business activities undertaken by the company.