The strong interdependency between carbon and energy markets has been well documented. The existing research reports asymmetric, time-varying and heterogeneous dependency in the short and/or long run between the carbon and energy market. The latest conflicts between Russia and Ukraine, and Israel and Hamas have had a significant impact on the demand and supply of energy assets. Geopolitical risk (GPR), as a noticeable example, evidently affects financial markets, energy, and commodity markets. We aim to study how the risk is transmitted to the carbon, energy market individually and as a whole unit. This study adopts the Baruník and Křehlík (2018) approach to discover the time-varying, heterogeneous dependency features exhibited in the higher-moment connectedness at different time scales - short and long-run. Furthermore, GARCH-MIDAS is applied to investigate whether there is asymmetric dependence between geopolitical risk and the carbon-energy network. Our results show a strong market-connectedness, asymmetric characteristics in risk spillover at higher moments. Natural gas and heating oil play an important role in risk spillover. In the long run, clean energy becomes the second-largest transmitter after natural gas. In terms of net spillover, carbon, heating oil are the main transmitters at lower moments, but clean energy undergoes a role transformation and becomes net- transmitter at higher-moment skewness and kurtosis. GPR significantly affects the carbon market, whereas clean energy is less impacted.