Energy poverty remains one of the key obstacles to sustainable development, directly affecting households and increasingly influencing business operations as well. The research investigates the relationship between energy poverty and greenhouse gas (GHG) emissions in the EU, addressing the often-overlooked connection between social vulnerability, environmental impact, and local climate policy. The study utilizes EU-level indicators to assess energy poverty across member states and develops the Energy Poverty Integral Index (EPII) to quantify it through multidimensional socioeconomic indicators. Building on this, the authors introduce the Energy Poverty and Emissions Index (EPEI), a novel, three-dimensional composite index that integrates (1) energy poverty (via the EPII), (2) residential GHG emissions, and (3) participation in the Covenant of Mayors (CoM), a proxy for local climate policy engagement. By bringing these components together, the EPEI offers a new perspective for examining the intersection of energy deprivation, carbon intensity, and policy responsiveness across the EU. This makes it possible to identify country profiles and policy gaps where high energy poverty coincides with either high emissions or weak climate action. The findings reveal significant correlations between energy poverty and emissions in several EU-27 countries, with strong positive relationships in the Netherlands, Lithuania, and Romania. In contrast, some member states exhibit inverse patterns. Cyprus, Italy, and Germany stand out with the highest energy poverty rates. The study contributes by proposing a standardized framework that links energy poverty to environmental and governance dimensions, supporting more targeted and just climate-energy policy responses in the EU.