This robe once belonged to Jedi Master Arren Kae before being passed on to her daughter Brianna sometime after her death at Malachor V during the Mandalorian Wars. Brianna, one of the Lost Jedi and companion of Meetra Surik, was once called the "Last Handmaiden" during her time in the service of Jedi Master Atris. Hence, the name of the robe.
In the game, Brianna becomes a companion only if the Exile is a male character. After the two spar for the first time, the Exile, while being dressed himself, must ask Brianna to get dressed and then she will don this robe. Brianna is the only character who is able to equip this item.