For those who haven’t seen the original trilogy in a while (there’s still time to marathon before Star Wars: he Last Jedi), the bun Billie Lourd is wearing is the same as the one Princess Leia wore at the Royal Award Ceremony on Yavin 4 at the end of A New Hope.
But for now, she has her own future and is already a part of the universe as Lieutenant Connix in Star Wars: The Last Jedi.
Billie Lourd, as seen in this Instagram post, definitely looks like Leia from the ceremony, so I could see fans favoring her to play a young Leia if the role came up in a future Star Wars film.
This is the awards ceremony after the destruction of the Death Star, where Princess Leia Organa bestows medals of bravery on Han Solo and Luke Skywalker (and for some reason leaves Chewbacca medal-less).