Emission trading schemes (ETSs) have become vital tools in striving toward global emission reduction objectives and promoting a sustainable economy. This paper empirically investigates the impact of market conditions on interconnectedness within precious metals, clean energy, green bonds, and carbon markets, focusing on China and the EU ETSs as the study subjects. A TVP-VAR-based asymmetric connectedness approach is adopted to capture the evolving relationships between the variables of interest in the time–frequency domain. The empirical findings reveal that: First, time-varying asymmetric connectedness and spillover effects among clean energy, precious metals, green bonds, and carbon markets are identified in both time and frequency domains under diverse market conditions, with long-term connectedness asymmetry being particularly sensitive, although spillovers exhibit variations. Second, the role and intensity of net transmitters or receivers vary across market conditions and frequency domains, indicating the complex and nuanced nature of market interactions. The EU ETS demonstrates a higher level of connectivity with global markets for clean energy, precious metals, and green bonds when compared to the Chinese ETS. However, it also shows greater susceptibility to fluctuations in market conditions. These results have significant implications for both investors striving to build sustainable diversified portfolios and regulators endeavoring to craft effective policies for risk regulation and sustainable development.