Conway didn’t want to challenge his congressman in Maryland, Rep. Jamie Raskin, who he said he loves, so the friend suggested he instead look at a seat in Manhattan that was soon to be vacant following the retirement of Rep. Jerry Nadler.

George Conway, who was once married to a former adviser to the president before becoming a prominent anti-Trump voice, announced on Tuesday that he is running for a U.S. House seat in New York City, t...