The "Transportation Emergency Relief Extension Act" aims to enhance flexibility for federal-aid highway emergency relief projects by amending title 23 of the United States Code. It introduces a new provision preventing the Secretary of Transportation from requiring projects to advance to the construction obligation stage before the end of the sixth fiscal year following an emergency declaration. This deadline provides states with more time to plan and execute recovery efforts after disasters. Furthermore, the bill allows for extensions to this deadline; the Secretary may grant an initial one-year extension upon a Governor's request and subsequent extensions if suitable justification is provided. To improve transparency and guidance, the legislation mandates that the Secretary update the Federal Highway Administration's Emergency Relief Manual every two years, distributing it to State departments of transportation and making it publicly accessible online.