This paper examines the time and frequency connectedness among electricity, carbon and clean energy markets, and oil price demand and supply shocks. In doing so, we use the spillover method proposed by Diebold and Yilmaz (2012) and its extension in the frequency domain by Baruník and Křehlík (2018). We find increased connectedness during the global financial crisis as well as in the shale oil revolution period. The total connectedness is also higher in the short-run compared to the long-run. Due to their low connectedness, electricity futures can act as a risk diversifier and safe-haven asset against oil shocks. Net pairwise directional connectedness among oil shocks and the clean energy index is higher during the shale oil revolution. These results have important implications for investors with different investment time horizons.