Natural gas is frequently introduced as a “transitional fuel”. Because burning natural gas emits less carbon dioxide emissions than burning either oil or coal. Additionally, the intermittent nature of low-carbon electricity generation creates imperative for using natural gas for power generation. The role of natural gas is currently under scrutiny as climate change transforms into a climate crisis. Meanwhile, share of natural gas in the primary energy consumption of Azerbaijan is 69%, while 94% of the country’s electricity is currently being generated in natural gas-fired power plants. In this manner, this paper estimates income and price elasticities of natural gas demand for the Azerbaijan case. In this study, various sets of estimation techniques are utilized. By modeling natural gas demand with different estimation methods, including Autoregressive Distributed Lagged Structural Time Series Modeling, Dynamic Ordinary Least Squares Method, Fully Modified Ordinary Least Squares, Canonical Cointegrating Regression, and General to Specific under Autometrics multi-path search machine learning algorithm, we try to find if there is room for the country to export more. All these utilized estimation methods confirmed the long-run income elasticity to be around 0.8, while the long-run price elasticity is around −0.1. Both estimations provide insights in terms of energy security and electricity security for policymakers during the implementation process of climate, energy, and environmental policy. Findings of this study classify natural as a necessity and normal good for the Azerbaijan case. The main policy implication of this study is that policymakers must enable and facilitate the availability of close renewable substitutes for residential and commercial customers. Estimated elasticities suggest that with rising national income, demand for natural gas will keep increasing, and efficient consumption will not be attainable with increasing prices. In the pursuit of export potential, findings suggest that it is more relevant to free up natural gas allocated from power generation by substituting it with renewable energy sources.