Never Yielding Europe's Territory (NYET) Act of 2022 This bill addresses Russia's actions against Ukraine and other countries in the region. The bill authorizes and expedites the provision of security assistance, including by (1) prioritizing delivering excess defense articles to Ukraine, (2) authorizing the Department of State to waive certain costs for defense articles leased to Ukraine, and (3) authorizing additional Foreign Military Financing for programs in Europe. The bill also provides funding for (1) Foreign Military Financing assistance to Ukraine, (2) the Global Engagement Center to counter foreign-sponsored propaganda and disinformation, (3) the Countering Russian Influence Fund to support Ukraine and other countries in response to Russia's aggression, and (4) International Military Education and Training assistance for Ukraine. Furthermore, the bill imposes sanctions, including on (1) senior Russian military officials responsible for planning or executing military operations that violated Ukraine's sovereignty or territorial integrity, and (2) foreign individuals or entities that acted on behalf of Russia's government to destabilize Ukraine or disrupt Ukraine's critical infrastructure. The bill also addresses additional matters, including (1) authorizing Radio Free Europe/Radio Liberty to explore opening new bureaus to reach audiences on Russia's periphery; and (2) providing for expedited approval of natural gas exports to qualifying nations, including NATO members, whereas currently expedited approval is only available for exports to countries that are in a free trade agreement relating to natural gas with the United States.