Joseph V. Melillo, the executive producer of the Brooklyn Academy of Music, saw Mr. Tennant’s performance for the first time recently, on video. “There’s a kind of gentleness in his acting, his interpretation, that you don’t often see,” he said by phone a few days later. “It’s not the kind of bravura physicality, it’s much more internalized and soft. It’s fascinating.”

Sheltered because he took the throne at the age of 10, Richard II was deposed at 32 and died in captivity the following year; Shakespeare’s play covers the last two years of his life.

“If you are in a world where the divine right of kings is a thing, and as a child you’re told, ‘God has chosen you to lead these people,’ and you’re then surrounded by acquiescence and adulation, what does that do to you?” Mr. Tennant asked. “How does that form the man you become? That’s what fascinates me about trying to find a center for who this character was.”

One of the things about Mr. Tennant’s portrayal that drew the most notice in Britain — and will be on display again in Brooklyn — was Richard’s cascading hair. (Accomplished with extensions in the original production, the ’do will be a wig this time around.) It was a choice in keeping with his rarefied approach to the character.

“I liked the idea that he would alight on something he found rather beautiful,” Mr. Tennant said. “He’s an aesthete. If he found it rather glorious, there’d be no one to challenge that it was wrong or unacceptable or not what men did. From that, we got the idea that he would have gold leaf on his fingernails. It was looking for a few things that would set him apart, because he could. Because no one would tell him he couldn’t.”

Sitting for an interview in a Manhattan hotel bar, a pot of tea at his elbow, Mr. Tennant was in town doing publicity for the Netflix series “Jessica Jones,” which had been released a few days earlier. (His villainous character, Kilgrave, possesses powers of mind control and is obsessed with the heroine.) Just before that he had taken part in his first read-through for the revival of “Richard II,” nearly two years after the British production closed.