Tps applications take up to a year or more to get approved. You can travel just fine while your application is pending.
Travel authorization for Temporary Protected Status (TPS) beneficiaries allows you to travel back to the United States and, if you are eligible, be inspected and admitted into TPS.
During a designated period, individuals who are TPS beneficiaries or who are found preliminarily eligible for TPS upon initial review of their cases (prima facie eligible): Are not removable from the United States. Can obtain an employment authorization document (EAD) May be granted travel authorization.
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.
Traveling to U.S. Territories. Undocumented individuals who hold a temporary protection (e.g. TPS/DACA-recipients) may travel to the U.S. Territories without Advance Parole.
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.
Travel to US territories such as Puerto Rico, the US Islands, Guam, and others does not necessitate obtaining advance parole or subjecting DACA recipients to the same restrictions that apply to international travel.
A work permit authorizes an employee to work in the US Islands specifically, while a work visa is issued for entry into the US Islands and may be required for the worker to legally enter and work.
Advance Parole that is granted in response to an approved expedite request will usually only be valid for the amount of time it takes to attend the emergency situation. Rather than the typical 2-year validity period, an emergency Advance Parole may only be valid for 1 month or several weeks.