How to distance from overly clingy friend without dropping her completely?

I (15f) am in a smaller friend group with a few girls I'm really close with, we've known each other for a long time and are really tightly weaven. Then, in October one of my friends (we can call her Karla) said that she was going to bring this girl from her social studies class who we will call "Avery" for the sake of the story. Avery (15f) said that her friends were being quite rude to her and excluding her, so obviously my friend wanted to be nice and let her sit with us.

Avery is an incredibly sweet girl, but most can notice she is not very developed in her social skills and can't read the room, and can't keep a secret. She unintentionally and backhandedly insults others or will sort of be insensitive, but not on purpose. I don't blame her though, and I believe that this is from her helicopter parents sheltering her. Her parents are quite strict. and because of this, it makes her get quite clingy and attached to others. (They cancelled her europe trip just because her sister and her were arguing for example)

She is is still sitting with us now, but has gotten quite invasive of me and Karlas personal space. She follows Karla into all of her classes and tracks her location via Snapchat, she has even gone as far to call Karla every time she is in the halls between classes just to find her whereabouts and has followed her even into the gym locker room. This constant following has made my friend Karla turn off her location and even firmly decline such behavior.

I have not really liked Avery as a person, but of course I'm going to be nice to her to be mature. But the whole situation has made the people in the friend group crack, and then only a week ago, Karla had a large outburst to an old group chat without Avery, expressing her annoyance.

It's not like we all don't like her, but every healthy friendship needs personal space, especially since we are all introverts.

How can we get her to lay off a bit more without seeming too overtly rude? And how should we establish firmer communication?

tl:dr A new girl (15f) who has joined my friend group has been invasive of our personal space and is constantly following my friend around, making her uncomfortable. How can we get her to be less clingy and following us excessively without being too abrupt or rude?