Ezra Klein, an analyst, columnist and television commentator who runs The Washington Post’s Wonkblog, is making plans to leave the newspaper after failing to win support for a new website he wanted to create within the company, according to four people with knowledge of the negotiations. Mr. Klein, who quickly ascended into the ranks of the Washington media establishment with a multiplatform blend of policy nuance and number-crunching on Wonkblog, approached Katharine Weymouth, the Post’s publisher, in recent weeks, the people said. After consultation with the newspaper’s editor, Marty Baron, according to one of the people, he put forward a...