The role of King Lear has become a virtual rite of passage for actors of a certain distinction and vintage. Over the past 20 years, I’ve seen Shakespeare’s ravaged monarch tackled by Christopher Walken, Frank Langella, John Lithgow, Kevin Kline, and Glenda Jackson, among others. So it’s hardly surprising that Kenneth Branagh, the British stage and screen star known for his affinity for and devotion to the Bard as both an actor and director, would get around to the task. 

For his new “King Lear,” which arrives at New York after a West End run last fall, Mr. Branagh juggles the title role with that of director. He shares the latter duty with Rob Ashford, a Tony Award-winning alumnus of both Broadway and London productions, and Lucy Skilbeck, a veteran of the Royal Academy of Dramatic Art — popularly known as RADA. That’s where Mr. Branagh himself studied and performed and, later, served as president.