I am dealing with something similar, a 'tween' who is hard to trust. I have told her that she doesn't need to trust anyone until she is ready and that I won't tell 'her' issues/stories to my t unless she approves it. I think it is a lot up to my t to work on trust issues, as most of the issues are her own. I act as a go-between and explain to my providers that she is having a hard time dealing with her own stuff, and that she doesn't want to share or talk, but that she needs to the most. I think she also knows that I am looking out for her best interest and will not force her before she is ready. Luckily she does trust me.

I would talk to your t about this issue and see what she has to say. I explain it that I am the only one who decided to go to therapy, and so some of the others are not as free-flowing as others.
Some random ideas to toss out (you obviously will choose what works/doesn't work for yourself)

1. telling t and trying to get the teen to tell your t why s/he doesn't trust, etc
2. writing to the teen or talking, and getting input on what is okay/not okay to talk about, and (hopefully) why
3. coming up with some sort of contract with the teen on ways to make it so that the rest of you can talk
4. asking t questions that may help the teen feel more at ease (especially if there is one or two things that make the teen suspicious)

Teens need to be as autonomous as they safely can, so a teen part may respond to having more of a say on things that aren't so important. For example giving a teen a couple chores and giving them options on when they decide to do them, or giving them three and having them choose two to get done, you get a lot more done around the house than if you simply dictate which chores need to be done. Taking this idea of giving choices, you may decide to give the teen the ability to write or talk to the t about concerns, but stress that it is important to communicate why. Or any variation of the idea.

Sorry if this is just a ton of rambling. I think it's great for any teen to decide to trust/not trust someone on their own. It's much better than a teen who has no boundaries. But it's also important to stress that the benefits of talking are there, and that other parts also need to have their choices respected. So if they wish to talk, it's important to let them, that kind of thing. It's good that your teen is making choices, but they also need to allow others those choices and they need to be encouraged into seeing the positives/benefits of therapy. It's difficult when the brain is at that stage of development to make peace with everyone.
Hugs!!
IJ