I wonder if Anne will lose the title
Princess Royal?
Maybe Charlotte will be the new Princess Royal?
Princess Anne will remain Princess Royal. The title will likely eventually be recreated for Charlotte, but only after Anne has died, and only after William becomes King - the Princess Royal has always been the monarch’s eldest daughter and is held for life.
The late Queen (as Princess Elizabeth) was never Princess Royal because the title was held by her Aunt Mary (Mary, Princess Royal and Countess Harewood) who did not die until 1965, and so held the title until then) - and Elizabeth was, of course, not just the eldest daughter of George VI, but also understood to be his very likely heir. It doesn’t get taken off somebody to be given to somebody else.