Against the backdrop of the exponentially growing trend in green finance investments and the calls for green recovery in the post-COVID world, this study presents the time-frequency connectedness between green and conventional financial markets by using the spillover models of Diebold and Yilmaz (2012) and Baruník and Křehlík (2018). Covering a sample period from January 01, 2008, to July 31, 2020, we aim to explore the dynamics of connectedness between conventional and green investments in fixed income, equity, and energy markets. Additionally, we determine the role of market-wide uncertainty in altering the connectedness structure by performing a subsample analysis for the ongoing COVID-19 pandemic crisis period. Our results show that competing energy investments are not connected, and there is only one-way spillovers from the conventional bonds in the fixed-income investments. Additionally, we observe a low (high) intergroup connectedness for conventional (green) investments. Moreover, the frequency-based analysis shows that connectedness between these competing markets is more pronounced during the short-run. The subsample analysis for the pandemic crisis period shows similar results except for the disconnection between bond markets in the short-run frequency. Our time-varying analysis shows peaks and troughs in the connectedness between climate-friendly and conventional investments that suggest different global events such as the Eurozone Debt Crisis and Shale Oil Revolution drives the association between alternate investments. Similarly, we observe an enhanced connectedness during the recent COVID-19 period, suggesting that financial stability would be a significant factor in determining the smooth transition to green investments.