One of President Donald Trump’s choices for a senior position in the White House is beginning work while facing a criminal charge after he allegedly tried to bring a handgun onto an airliner last year, court records show.

Sebastian Gorka, a national security and terrorism analyst, was stopped at Ronald Reagan Washington National Airport in Virginia last January by an officer with the U.S. Transportation Security Administration, who detected a 9mm caliber handgun using X-ray equipment as it passed on a conveyor belt. The officer...