New START Treaty Improvement Act of 2019 This bill prohibits extending the Measures for the Further Reduction and Limitation of Strategic Offensive Arms (New START treaty) or any successor agreement unless the agreement (1) includes and is signed by China, and (2) covers all Russian strategic and non-strategic nuclear forces. (The New START treaty between the United States and Russia is set to expire in February 2021 but may be extended to February 2026.)