John F. Kennedy’s grandson Jack Schlossberg is running for the U.S. House of Representatives next year, announcing Tuesday that he’s seeking a congressional seat in New York City that will be vacated by longtime Democratic Rep.

Another Kennedy has entered the political ring.

“It’s a crisis at every level, a cost-of-living crisis sponsored by the big, beautiful bill, historic cuts to social programs working families rely on health care, education, childcare, a corruption c...