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.

The headline on the program cover for the New York production, at the Hudson Yards venue The Shed, reads, “Kenneth Branagh in King Lear.” The playwright’s name is listed below the title, above a picture of the leading man, shown bearded and brooding; even with his tattered garments and slightly mussed hair, he looks more like an action hero than a tortured, cognitively deteriorating old man.

Mr. Branagh’s performance, too, betrays a certain vanity. The role invites a degree of preening, to be sure, to say nothing of the extremes of sorrow and rage required. Even when those extremes surface, though, this Lear manages to sustain a strangely regal air. Ålso, I couldn’t help but notice, as those garments were battered and shed in the storm in Act Three, that the star’s preparations for playing an elderly fellow in failing health don’t seem to have included avoiding the gym.

To Mr. Branagh’s credit, his Lear is among the wittier ones I’ve seen, with the actor savoring the bleakly comedic aspects of his character’s descent into folly. And with Mr. Ashford and Ms. Skilbeck, he oversees a crisp, brisk production — the tragedy is presented in just two hours here, without an intermission — that manages to feel of the moment without getting weighed down by any anachronistic schtick.

The contemporary vibe owes much to the young, racially diverse cast, which finds Mr. Branagh surrounded by recent RADA graduates. Deborah Alli and Saffron Coomber scheme and spar compellingly as wicked sisters Goneril and Regan, respectively, with Ms. Coomber’s icier presence serving as a neat foil to Ms. Alli’s relative, and plainly superficial, warmth.

In contrast, Jessica Revell brings transparent compassion and a gentle but firm resolve to the play’s pair of truth tellers: Lear’s youngest and only faithful daughter, Cordelia, and his loyal Fool. Joseph Kloska is a sturdy, sympathetic Earl of Gloucester; Doug Colling proves at once ingenuous and robust as Gloucester’s devoted son, Edgar; while as Edgar’s dastardly, illegitimate half-brother, Edmund, Dylan Corbett-Bader practically sweats unctuousness.

Jon Bausor’s vast, stark set features spiky stones and an enormous disc that provides a surface for Nina Dunn’s atmospheric, often eerie projection design. If these elements can suggest a trip into outer space — or back to ancient Britain — Mr. Branagh and his collaborators ensure that this production stays rooted squarely on earth and in tradition, even as they maintain a youthful energy. This may not be the most intriguing or moving “King Lear” you’ll ever see, but you won’t be bored.