President Trump said on Thursday that he would nominate Jay Clayton, the U.S. attorney in Manhattan and the former chairman of the Securities and Exchange Commission, to be the next director of national intelligence. Mr. Trump had been under pressure to move on from his decision to appoint Bill Pulte, a top housing official, as the acting director, replacing Tulsi Gabbard, who announced last month that she would step down from the post. The appointment of Mr. Pulte derailed the congressional reauthorization of one of the government’s most powerful surveillance authorities. But the announcement of Mr. Clayton to be nominated...