We investigate how green energy supply chain vulnerabilities (GESCV) amplify climate-related risk exposure among major energy firms across 36 countries from 2010 to 2023. Our benchmark model substantiates that GESCV amplifies corporate exposure to climate-related risks, with risk quantified using the Fama-French Three-Factor model. The adverse effects remain pronounced in developing countries, fossil fuel-based firms, and high-climate policy uncertainty groups. Mechanism-wise, GESCV heightens climate-related risk exposure by diminishing total asset turnover and worsening investment inefficiency. Further analysis reveals that governance quality is the only significant factor mitigating the detrimental link between GESCV and climate risk exposure, whereas women's political empowerment and environmental technologies exhibit minimal influence. Additionally, a difference-in-differences (DID) model confirms that the Paris Agreement has played a role in easing the negative consequences of GESCV on climate-related risk exposure. These findings underscore the need for governance enhancements, diversified supply chain strategies, and policy-driven investments in green technologies as essential measures to curb climate risks during the global energy transition.