Travelers who are fully vaccinated or who recovered from COVID-19 in the past 3 months do not need to get tested before departing the United States for international travel or before domestic travel unless their destination requires it.
Public Health Guidance for Potential COVID-19 Exposure Associated with Travel
www.cdc.gov > coronavirus > 2019-ncov > php > risk-assessment
Everyone, especially those at increased risk of severe illness from COVID-19, and people who live with them, should avoid non-essential travel. Travel increases your chance of spreading and getting COVID-19. CDC recommends that you do not travel at this time.
Daily Activities and Going Out | COVID-19
www.cdc.gov > 2019-ncov > daily-life-coping > using-transportation
Although vaccination requirements are set by countries, not airlines, airlines are not allowing passengers to check in for international flights without first verifying whatever documents are required, including vaccination records and virus tests.
Help! I'm Traveling to Europe. All The Required Documentation Is Dizzying - The New York Times
www.nytimes.com > europe-covid-vaccine-flights-planes-travel-vacation
Air passengers traveling to the US are required to present a negative COVID-19 test result or documentation of recovery. Airlines must confirm the negative test result or documentation of recovery for all passengers before boarding. If a passenger chooses not to present a test result or documentation of recovery, the airline must deny boarding to the passenger.
Requirement for Proof of Negative COVID-19 Test or Recovery from COVID-19 for All Air Passengers Arriving in the United States
www.cdc.gov > 2019-ncov > travelers > testing-international-air-travelers