President Donald Trump will give a nationally televised address Monday night to unveil his strategy for the long-running war in Afghanistan, the White House said, a plan expected to include sending as many as 4,000 more troops to the country.

He’ll deliver the prime-time speech from Fort Myer in Arlington, Va., using the same sort of high-profile stage that his predecessor, Barack Obama, employed in laying out a new approach to the war in 2009. Mr. Obama delivered his speech before a national television audience at the U.S....