[This post contains details from Doctor Who season 9 that may be considered SPOILERS.]
Season 9 of Doctor Who ended with Maisie Williams' Ashildr/Me in an interesting place. Some fans believed that this might be a setup to bring her back as a full-time companion in the next season, especially given the connection that the season built between her character and the Doctor.
Williams herself recently commented on the rumor. Unfortunately for fans who were keen to see her riding around in the Doctor's TARDIS, she confirmed that she won't be back in the new season.
Season 9 of Doctor Who ended with a resurrected (on a technicality) Clara Oswald and Ashildr travelling the whole of time and space in (yet another) stolen TARDIS. While the dialogue between the characters indicated that Clara would eventually go to meet her fate in Face the Raven, it's unlikely that Ashildr would relinquish a TARDIS that easily. This set up an easy path for her to be a recurring character and eventual companion in season 10, even if Clara didn't return. According to Williams, though, that's not going to happen:
"I’m not going to be working on Doctor Who again. Everyone’s hyping about it, which is very exciting, but I guess that’s more of a publicity thing. But no, I’m not going to return, I have a lot of other really exciting projects lined up instead."
A companion role on Doctor Who would have been a stretch for Williams regardless, between her commitments to Game of Thrones and other upcoming projects like The Forest of Hands and Teeth and Arrivals. Even a role as a recurring character may have been difficult if some of the "other really exciting projects" she referred to haven't been announced yet. With Williams announcing that she won't be back, it looks like we'll be getting a wholly new companion after all.
As entertaining as continued interactions between the Doctor and Ashildr may have been, a new companion for season 10 is likely more fitting in the end. Given that the season will be the last for both Peter Capaldi and showrunner Steven Moffat, a new companion could serve the carryover role that Clara herself served when the Eleventh Doctor regenerated into Capaldi's Twelve. Of course, who that companion will be, whether it will be male or female or if it will even be human is still in the realm of rumor so far.
With no new season scheduled for 2016, fans will have a bit longer to wait until the question of the next companion is answered. It's possible that the companion will be introduced in the 2016 Christmas special, though the companions during these specials have more often than not been of the one-off variety. Still, there are a few instances of companions introduced in the Christmas specials who later came back to the TARDIS, so it's always possible.
Doctor Who returns in December with a 2016 Christmas special, followed by season 10 in 2017.
Source: Bang Showbiz, via CinemaBlend