President Donald Trump’s imprint on the federal judiciary could soon expand, after the announcement of five appellate and eight district court nominees.

Trump has made 69 federal judicial appointments, including U.S. Supreme Court Justice Brett Kavanaugh, whose confirmation in the face of allegations of sexual assault and perjury divided the country.

The new appellate nominees are to two of the nation’s most important courts—the U.S. Court of Appeals for the Second Circuit, whose territory includes New York, and the Ninth...