Director Alpha is an A7M1 model—the first of her kind in the A7 series, which is also where she gets her name. Robots in this world typically take their owner's name, so it's possible Sensei or someone in his family originally owned her. She wears a pendant that matches Sensei's, adding to the mystery. Kokone has mentioned that the A7M1 earned the nickname "the Phantom" at some point, though what that actually means or how she got it remains unclear. Beyond that, her origins and original purpose are largely unknown.
These days, Director Alpha serves as director of Taapon, a stratospheric aircraft that circles the globe monitoring changes to the world below. There are hints that she'll be the last living person aboard—since she doesn't age like the rest of the crew, she'll outlive them all.
One odd thing that's been noted: Director Alpha seems to share a strong mental connection with Alpha Hatsuseno, though neither of them appears to realize it's happening.
Content compiled by AnimeList.moe from publicly available sources.