We investigate the dynamic extremal connectedness of sectors within the Chinese stock market conditional on exogenous extreme risk through multivariate extreme value regression. To proxy the exogenous extreme risk, we independently consider market volatility-based measures and policy uncertainty-based measures. We discover that market volatility-based measures have a stronger influence than policy uncertainty-based measures on the extremal connectedness of sectors. The oil volatility index is the most influential on extremal connectedness, and the energy sector plays a direct role in transmitting exogenous extreme risk. Our findings provide new insights into understanding the drivers of systematic and idiosyncratic contagion.