Political asylum
From Memory Alpha, the free Star Trek reference.
Political asylum, usually called simply asylum, is a diplomatic procedure by which a sovereign entity grants someone protection from a hostile force.
In 2366, when Admiral Alidar Jarok's Romulan scoutship was pursued by a Romulan warbird and he reached Federation space and requested asylum aboard the USS Enterprise-D. (TNG: "The Defector")
In 2367, the Kaelon Timicin requested asylum aboard the USS Enterprise-D in an attempt to challenge the ritualistic suicide custom called The Resolution. The same year, Klingon Ambassador Kell requested asylum aboard the USS Enterprise-D after he was exposed as an operative working for the Romulans. Captain Jean-Luc Picard, however, would not grant asylum unless he was found innocent of any involvement in the attempted assassination of Governor Vagh. (TNG: "Half a Life", "The Mind's Eye")
In 2368, Commander William Riker asked the J'naii leader Noor to allow Soren asylum onboard the USS Enterprise-D in lieu of psychotectic treatment. (TNG: "The Outcast")
In 2369, the terrorist Tahna Los requested asylum from the Federation against the Cardassians. The same year, Miles O'Brien encouraged Tosk to request asylum, Tosk instead chose to die with honor. (DS9: "Past Prologue", "Captive Pursuit")
In 2372, while in the Delta Quadrant, the USS Voyager encountered Quinn, a member of the Q Continuum, who requested asylum from Captain Janeway. Although it was unclear how exactly Janeway could protect him from the other Q, she acquiesced. (VOY: "Death Wish")
