Not weird at all. I saw my T at a university counseling center first (she was a staff psychologist there) and then eventually followed her to private practice. I bet your old T would remember you. Eight sessions within the last few years is likely to stick in her mind. But either way, you would likely have to go through the intake process (forms, psychological history, etc) at the new practice. My T definitely remembered me and my background, and we still had to do all that. (I also signed a form releasing the therapy records she wrote to her, which amused me.)

My only concern would be whether somebody fairly new to the profession would have the training and experience to adequately help you. I know you mentioned before that you weren't sure that your most recent T had the background necessary to help with everything you wanted to work on. So you could potentially consider starting the T search over to find somebody who has specific experience with eating disorders or substance use issues, if that does not describe either of your former Ts. I say this mostly from my own experience of having several lovely, well-meaning, dedicated student therapists who just didn't have what it took at that point in their careers to help me very much. (I was/am a slightly more complicated case than a first-year student with homesickness and roommate conflicts.) My current T is middle-aged with like twenty years of experience doing therapy, and it makes a huge difference in how she works and in how confident I feel that she can handle whatever I throw at her.

Hopefully this is not too far off-topic or out of place, but I have seen your Dear T posts, and my heart goes out to you. Have you considered looking into getting a T to fill the gap while you are studying abroad? If your counseling center can't offer you services, can you ask the study abroad office if they have suggestions? Or if you have health insurance, you might be able to find a T in private practice who can do Skype or phone sessions while you are away. It is becoming more common for therapists to offer that. Being away from home when you're already going through some mental health stuff sounds so stressful. I know you want to make your T proud by going it on your own, but I don't think she would want you to struggle needlessly. In fact, getting help and support for yourself is way more impressive than trying to white-knuckle your way through. There's no shame in asking for help.