Climate change is a significant concern in the contemporary world. It has become a critical issue worldwide in countries, organizations, industries, and financial markets. This study investigates the effect of the relationship between climate risks (CRs) and climate policy uncertainty (CPU) on ESG stocks in both emerging and developed markets. Using the asymmetric TVP-VAR technique, this study analyzes the dynamic nature of these connections. Monthly data on climate policy uncertainty and climate risks were obtained from economicpolicy.com, while ESG leader indexes from the S&P 500 were collected for the period 2013–2023. The findings reveal that climate policy uncertainty (CPU) and physical risks (PRIs) exhibit a negative connectedness with ESG stocks, implying that rising uncertainty and physical climate threats negatively impact the performance of ESG stocks. In contrast, transition risks (TRIs) display a positive connectedness with ESG stocks, suggesting that as economies transition toward low-carbon policies and sustainable practices, ESG investments benefit from these structural changes. This study suggests that policymakers and market participants should take proactive measures to mitigate climate policy uncertainty and address physical climate risks to enhance the stability of the ESG market. This is particularly crucial for emerging markets, where these effects may be more pronounced. By managing climate-related risks effectively, policymakers can foster a more resilient ESG investment environment, ensuring its long-term stability and investor confidence in sustainable markets.