The Exile is a former Jedi commander who served in the Mandalorian Wars, and under Revan. A mysterious woman who tends to keep to herself, the Exile joins the party after hearing about the Doctor's attempts to find Revan. She can be found on Etti VI, after it is discovered that there are new leaders in the Genoharadan. A messenger will rush up to you to inform you one of the companies' freighters is being attacked. This will allow you to then board the Ebon Hawk, where she's located.
To recruit her, you must defeat the boarders (who appear to be Worshippers of Freedon Nadd) (in the 1.0 version its the troopers of the True Sith, the Screamers and the Rakghouls) and then talk to her on her ship, the Ebon Hawk. The Hawk can be found in the merchant district, on a dedicated landing pad across from the entry into the cantina.