Many directors of Shakespeare films have not been great film innovators and stylists—they've been stage directors with a deep understanding of the plays. That combination is enough to produce a great Shakespeare movie. But there's another group of directors who have both a deep understanding of the plays and who are also great film stylists and innovators.
At the summit of that group are two directors: Orson Welles and Akira Kurosawa. Welles had directed most of Shakespeare's history plays by the time he was fifteen, and he reread the plays throughout his life. His three feature-length Shakespeare films may be the best things he ever did. He thought, and I agree, that his greatest film wasn't Citizen Kane but The Chimes at Midnight, his mash-up of the Henry plays.
Similarly, Kurosawa's appreciation of Shakespeare began early, when he was an art student, and continued throughout his life. Three of his best films are versions of Shakespeare plays. The Bad Sleep Well loosely follows Hamlet, resetting it in postwar Japan. Ran ("Chaos") is an adaptation of King Lear set in sixteenth-century Japan. And Throne of Blood is a Macbeth adaptation, also set in feudal Japan, that follows Shakespeare more closely than either of the other two films.