Facing an impeachment inquiry at home, President Trump is heading to London for a different political challenge: a meeting of the North Atlantic Treaty Organization.

Mr. Trump, who as a candidate labeled the alliance obsolete, has upended past gatherings with his complaints that members must spend more on defense. But his White House struck a more conciliatory tone ahead of the Dec. 3-4 meeting to mark NATO’s 70th anniversary, taking credit for increased military spending by member countries and declaring that the “trans-Atlantic...