In recent decades, there has been a positive trend in world politics in the field of promoting territories’ sustainable development. At the same time, one of the most relevant areas is to promote the transition to renewable energy sources (RES), which correspond to one of the UN’s goals—Sustainable Development Goal 7 (SDG 7) “Ensuring universal access to affordable, reliable, sustainable and modern energy sources for all”. This article is devoted to the study of the renewable energy sources’ impact on the sustainable development of the Russian Arctic zone. The authors chose the level of carbon dioxide (CO2) emissions as an indicator reflecting the impact of RES on sustainable development, since this factor is one of the main factors for assessing trends in the activities of countries aimed at achieving progress on most of the Sustainable Development Goals of territories. The hypothesis of the relationship between the use of renewable energy sources and the achievement of progress on the Sustainable Development Goals, one of the indicators of which is the level of CO2 emissions, was tested and confirmed. An econometric analysis of panel data for 15 countries that are actively implementing the concept of sustainable development, including decarbonizing policies, was carried out, where the resulting indicator for achieving progress on the SDG was the amount of CO2 emissions. The factors influencing the resulting variable were indicators selected based on a review of existing models, as well as indicators of the Sustainable Development Goals’ achievement. Using an econometric analysis of interdependence, the indicators of progress towards the Sustainable Development Goals that are more likely to have an impact on the level of CO2 emissions were identified. These are electricity consumption, the share of renewable energy sources in the energy balance, the average per capita income of the population, and carbon intensity. Based on the results obtained, it can be concluded that renewable energy sources are a factor contributing to the achievement of progress on the Sustainable Development Goals. The results obtained are also applicable to the Arctic region, since all countries that have territories in the Arctic zone adhere to the policy of decarbonization and try to reduce the use of fossil fuels.