New York state’s attorney general, to date one of the most vocal antagonists of President Donald Trump, is preparing to escalate his office’s litigation against the president’s administration.

Democrat Eric Schneiderman has hired one of the top public-corruption prosecutors under former Manhattan U.S. Attorney Preet Bharara to focus specifically on issues involving the Trump administration. Howard Master, who prosecuted the Manhattan U.S. attorney’s case against longtime New York state Assembly Speaker Sheldon Silver, is expected...