Contrary to previous research, this study examines the transmission mechanisms between daily trade policy uncertainty (TPU), geopolitical risk (GPR), global financial stress index (FSI) and the three Australian financial markets (i.e., conventional, sustainable, Islamic stock markets) by using the quantile time-frequency connectedness approach. We also utilize the DCC-GARCH-t copula approach to examine the hedging effectiveness of the Australian sustainable and Islamic financial markets against the Australian conventional market's long-term volatility during high and low uncertainty. The time domain QVAR approach show that the Australian sustainable financial market returns receive the highest spillovers of shocks from TPU, FSI and GPR at the lower, medium and higher quantiles. Moreover, in the short term, at the lower quantiles the sustainable financial market receives the highest error variance contributions from FSI, while at higher quantiles, TPU, FSI and GPR transmit higher spillovers of shocks towards the sustainable market. Similarly, in the long term, the sustainable market receives the highest contributions to the error variances from TPU, FSI and GPR (GPR and TPU) at the lower (higher) quantiles. Moreover, at the lower, middle and higher quantiles, a shock in the Islamic (sustainable) market returns causes the highest contribution of error variances in the conventional market, compared with the (sustainable) Islamic market in the short and long run. Finally, the hedging strategy results show that investment in the Islamic financial market is the cheapest hedge against the long-term conventional market risk during high and low uncertainty periods.