#violet book

Rachel for Violet Book in 2018.

And a bonus behind the scenes:

I've seen a lot of people remark that she seems like she'll be a significant character because she's wearing the colors of both versions and her earrings have the terastalization logo (which is also the logo for the DLC as seen above).

I think she's going to be revealed as Heath's descendant, and that she will be looking to continue his work.

The most obvious thing is probably the hair since it's how a lot of the Pokémon descendants can be identified, and it's a pretty spot on match. I think the part that gives it the most weight, though, is the link between their names.

Briar is a type of wood that comes from the Erica Arborea, a shrub more commonly known as Tree Heath (and is a member of the heath or Heather family ericacea). Her name literally implies she descended from Heath.

Since Briar is a type of wood, I think she'll be playing a more significant role than just a teacher at Blueberry Academy. I think her name implies she'll be taking on the role as the new Professor in the absence of Turo/Sada (maybe unofficially or only narratively). My guess is that her interest in Terastalization is either due to it finally vindicating her family or because she knows something that Heath never wrote in the book.

I have more I want to add but I'll make an addition to this post since I've made my original point already.

TL;DR: I think Briar is Heath's descendant based on the hair and her name being wood that comes from a type of heath, and that because she's named after a wood she'll be a bigger role like a professor.