The Duchess Of Cambridge (when the show was made) is Kate Middleton, the wife of Prince William (first in line to the UK and Commonwealth throne). She is mentioned (disparagingly) at 32.45.
She became The Princess Of Wales on September 2022 after her husband's grandmother, Queen Elizabeth II passed away.
This episode was released on May 5 2023, the day before her father in law, King Charles was to have his coronation.