In this article, we examine the spillover effects and connectedness among four prominent sustainability-related indices. We analyze daily data spanning from August 8, 2014, to April 12, 2023, to explore the interrelationships among the Green Economy Index, the World Environmental, Social, and Governance Index, the Global Environment Index and the Global Clean Energy Index. Particularly, we observe a clustering characteristic where both the Green Economy Index and the World Environmental, Social, and Governance Index exhibit a net- contributing behavior, especially during and after the COVID-19 outbreak. Global Environment Index, on the other hand, exhibits a net-receiving role, which became strong during the COVID-19 outbreak. Further, the Global Clean Energy Index demonstrates a neutral role, although it shows a net-receiving trend after the year 2022. Finally, dynamic analysis confirms the evolving nature of these interconnectedness measures, highlighting their sensitivity to events and shifting economic conditions over time.