Yes, if you have TPS, you can apply for advance parole to travel abroad by filing Form I-131 and getting approval before leaving the U.S.

Sure, TPS holders can apply for advance parole to travel abroad, but they must get approval from USCIS before departing the U.S.

Yep; you can apply for advance parole by filing Form I‑131 with USCIS and must obtain approval before traveling abroad.