Amane Kaunaq started out as one of the galaxy's top supermodels, but she got sick of it—burned out, disgusted, the whole thing. She bailed and joined the Galaxy Police instead, where she turned out to be genuinely excellent at the job. Her clean record was so spotless that people started calling her "the Zero Goddess" because she basically never ran into pirates. She was on track for a promotion to Detective 1st class when things fell apart.
The problem started when she landed her ship in a lake near Tenchi Masaki's place and pulled Seina Yamada out of the water. Thinking Tenchi was training the kid, she handed Seina an application to the G.P. Academy on the spot—and gave one to Tenchi too. Turns out there's a regulation against admitting citizens from underdeveloped planets, and her screwup tanked her promotion. Instead of moving up, she got assigned as an instructor at the Academy alongside Kiriko Masaki and her childhood friend Seiryo Tennan. (Tenchi got a pass because of his Jurai Royal Family connections, but that's another story.)
Amane can't stand Seiryo. Yeah, they knew each other as kids, but he's an idiot who tried putting the moves on her years back, and she's made it clear—repeatedly, often with her fists—that she wants nothing to do with him.
When Seina needed body modifications to survive Academy training, he moved into Amane's house along with Kiriko and a girl named Erma (who was actually the space pirate Ryoko Balta, undercover and spying on him). Before long, Amane's life basically revolved around Seina. The G.P. had figured out that his ridiculously bad luck attracted pirates like a magnet, so they decided to weaponize it—send him out, watch the pirates come, and use that to keep the galaxy peaceful.
Amane comes from money. Her family runs one of the galaxy's top fashion houses, and she originally joined the G.P. partly just to tick off her old-school father, who never stopped trying to get her back into modeling. When her family sponsored a G.P. fashion show years later, she made a brief comeback on the runway. But her father finally came around after watching her work with the latest G.P. battle gear in a live-fire demo—he admitted she'd made the right choice. He still hasn't totally let go of the modeling dream, though.
She's connected to the Kuramitsu family of Seniwa through her family's friendship with them, and she knows both Mihoshi and her brother Misao. Amane actually trained Misao back in the day and still calls him "Rookie."
Content compiled by AnimeList.moe from publicly available sources.