My person theory on Missy is that she’s been sent by Missy (unaware of course) to “train” The Doctor to become a perfect soldier. C’mon, Missy must be building an army. All of those Cybermen just for show? No. Anyway, I think that Missy “chose” her to train him in TBOSJ when she gave Clara the number of the TARDIS. Come on, Clara does act really bossy towards The Doctor, is a bit of a control freak and isn’t afraid to “have a go” at The Doctor or hit him. The traits of a Seargent. Also, the fact that there’s an ongoing theme of whether The Doctor is a “good man” or not.
Remember when Clara says: “Waste no more time arguing about what a good man should be”?
Clara is trying to turn the Doctor into a Good Man.
There’s also the fact of there being a GATE in the Nethersphere, which Missy is the keeper of. The gate must be a gateway somewhere. I think it’s a gateway to Gallifrey, and that Missy is building up an army to fight The Time Lords. With The Doctor against them.