TSA Security Threat Assessment Application Modernization Act This bill requires the Transportation Security Administration (TSA) to standardize the enrollment and renewal system for individuals applying for or renewing multiple TSA Security Threat Assessment programs, including the Transportation Worker Identification Credential, Hazardous Materials Endorsement, and TSA PreCheck programs. The standardization shall permit an individual to (1) enroll at a TSA-designated universal enrollment center once and use the application for one of such programs to enroll in two or more of such programs,with specified exceptions for those applying for or renewing enrollment in more than one program at different times; (2) apply successful, valid clearance results from a TSA Security Threat Assessment to satisfy vetting requirements for participation in any related program without additional cost; and (3) undergo a streamlined and expeditious renewal process. Additionally, the TSA must publish on its website information relating to the standardization of the enrollment system.