American Leadership in Space Technology and Advanced Rocketry Act or the ALSTAR Act This bill directs the Marshall Space Flight Center of the National Aeronautics and Space Administration (NASA) in Huntsville, Alabama, to provide national leadership in rocket propulsion by carrying out specified activities, including: contributing to interagency coordination to preserve critical national rocket propulsion capabilities; collaborating with industry, academia, and professional organizations to most effectively use national capabilities and resources; monitoring public- and private-sector rocket propulsion activities to develop and promote a strong, healthy rocket propulsion industrial base; and evaluating and recommending new rocket propulsion technologies for further development.