Current and former Justice Department officials, ex-U.S. Supreme Court clerks, and attorneys with Big Law pedigrees rounded out President Donald Trump’s latest list of planned judicial nominations June 7.

Four women also were included in the list of names Trump intends to send to the Senate, including three appeals court selections and seven for federal district court seats, the White House said.

The president also nominated two candidates to the U.S. Court of International Trade, which could find itself in...