If you are a permanent or conditional permanent resident who has been outside the U.S. for one year or longer, apply for a re-entry permit before you travel. Use Form I-131 - Application for Travel Document. For permanent residents, the re-entry permit is valid for two years from the date of issue.
If you have a green card, it's not necessary to carry a passport with you for domestic travel within the United States. That said, it's never a bad idea to have plenty of documentation, and if you have a passport, you may wish to keep that with you throughout your domestic travel as well.
While passports issued by governments are the most common variety of travel document, many states and international organisations issue other varieties of travel documents that allow the holder to travel internationally to countries that recognise the documents.
ESTA is an automated system that determines the eligibility of visitors to travel to the United States under the Visa Waiver Program (VWP). Authorization via ESTA does not determine whether a traveler is admissible to the United States.
A Travel Authorization (TE) is used to request approval for a business-related trip. In this document, the traveler indicates trip destination(s), purpose, and dates of travel and requests advance checks. In response, the TE records trip information and schedules advance checks.
Applications may be submitted at any time prior to travel to the United States. The Department of Homeland Security recommends that travel authorization applications be submitted at least 72 hours prior to travel.
What documents do I need to travel outside the United States? In general, you will need to present a passport from your country of citizenship or your refugee travel document to travel to a foreign country. In addition, the foreign country may have additional entry/exit requirements (such as a visa).
Electronic System for Travel Authorization (ESTA) Visa Waiver Program travelers are required to apply for and receive an approved travel authorization via ESTA to board a plane or vessel bound for the United States. (A travel authorization via ESTA is not a guarantee of admission into the United States.
The travel document usually arrives within 150 days (sometimes longer) after submitting your application. You can't leave the country until you have your approved travel document in hand, so you should expect to spend the 3–5 months after submitting your green card application in the United States.