I don’t think Chelsea will ever run for pubic office unless it’s something where she is in a 95% Democrat district, ala AOC’s win. And I think she thinks a plain old House seat is beneath her. She’ll simply remain a talking head ... spouting BS.
As I understand it, the Clintons planted Chelsea in Nita Lowey’s Congressional District. Nita stepped aside so Hillary could run for the NYS Senate seat, having not lived a single day of her life in NYS (vs native Nita). If asked, I am sure Nita would step aside from her House seat for Chelsea. She’s a good, loyal Commie. Oops, I mean Dem.