In “Circus Windows” and the “Spring Special”, Claire was in uni at the London School of Economics, which she hated but felt obligated to. Lottie’s visit in the “Spring Special” liberated Claire from the shackles of parental expectations, and she transferred to Sheffield between terms.

As of the “Autumn Special”, Claire had started studying sociology at Sheffield University with Lottie freeloading off her. I believe that’s still Claire’s situation, though we haven’t seen much of her school life since she got Lottie out of her dorm and set up in her own place. She seems to be spending all of her free time with Lottie and Glenn.