Compressed Gas Cylinder Safety and Oversight Improvements Act of 2021 This bill expands requirements for foreign manufacturers of cylinders used for transporting hazardous materials in the United States (e.g., compressed gas cylinders). Current regulations require foreign manufacturers to apply for authorization from the Pipeline and Hazardous Materials Safety Administration for testing such cylinders outside of the United States. This bill requires that, to obtain an authorization, manufacturers must meet minimum levels of financial responsibility and answer in their applications specified questions, including whether the manufacturer is or has been subject to various civil or criminal penalties. The administration must publish each application in the Federal Register for public comment and must also annually publish a list of authorized manufacturers online. The bill limits an authorization to one year; however, the administration may extend an authorization for five years if the manufacturer (1) complies with applicable requirements for at least three years; and (2) meets conditions regarding the accuracy of its application, sufficiency of its financial responsibility, and other matters. The administration may suspend or terminate an authorization if a manufacturer impedes an inspection or knowingly or intentionally provides inaccurate application information. The administration must also establish a process whereby an interested party may petition for a reevaluation of an authorization if that party has evidence of inaccurate or fraudulent information in the manufacturer's application.