The Transportation Emergency Relief Extension Act aims to increase flexibility for federal-aid highway emergency relief projects by amending title 23, United States Code. It establishes new provisions regarding project timelines and the dissemination of guidance. The bill prohibits the Secretary from requiring emergency relief projects to reach the construction obligation stage before the end of the sixth fiscal year after an emergency declaration, while also allowing for extensions upon a Governor's request with suitable justification. Furthermore, it mandates that the Secretary of Transportation update the Federal Highway Administration's Emergency Relief Manual every two years. This updated manual must be provided to all State departments of transportation and made publicly available on the Secretary's website, ensuring current guidance is accessible for emergency response and recovery efforts.