“Job,” a two-character thriller about a psychological evaluation going awry, started small, with a run last year at SoHo Playhouse. Word-of-mouth was good, the New York Times review was positive and sales were strong, so early this year it transferred for another Off Broadway run at the Connelly Theater in the East Village.

Now the play, written by Max Wolf Friedlich and directed by Michael Herwitz, is planning to make the leap to Broadway, with a two-month run beginning this summer at the Hayes Theater.

The Broadway production, like the Off Broadway runs, will star Peter Friedman and Sydney Lemmon. Both of them appeared in the HBO series “Succession” — Friedman was a member of the principal cast, playing Frank Vernon, the chief operating officer of Waystar Royco, and Lemmon appeared in the show at one point as a love interest of Kendall Roy.

Friedman is a mainstay of the New York stage who was nominated for a Tony Award for “Ragtime.” Lemmon has worked mostly onscreen, including in the Hulu streamer “Helstrom”; if her surname sounds familiar, that’s because she is also the granddaughter of the great actor Jack Lemmon.

In “Job,” Friedman plays a therapist who has been hired to evaluate Lemmon’s character for her suitability to return to work. (She has been suspended after a videotaped workplace breakdown.) Their interaction is fraught, and frightening, from the get-go.

“Job” is scheduled to begin previews July 15 and to open July 30 at the Hayes Theater, which, with about 600 seats, is the smallest house on Broadway. The run will be brief — it is scheduled to end on Sept. 29.

The play is being produced by Hannah Getts, who has been with the show at each stage of its production history; Alex Levy, a speechwriter and media strategist whose work includes communications consulting for New York Times executives; Craig Balsam, who co-founded the music company Razor & Tie; and P3 Productions, the company that was the lead producer for last season’s musical “How to Dance in Ohio.”

“Job” will be the latest sign of a surge to the stage by “Succession” alumni. Those include two of this year’s Tony nominees — Jeremy Strong, who played Kendall Roy on “Succession,” is nominated for “An Enemy of the People,” and Juliana Canfield, who played Kendall’s assistant, Jess, is nominated for “Stereophonic.”

Also on Broadway, Natalie Gold, who played Kendall’s ex-wife, Rava, is featured in “Appropriate.”

Meanwhile in London, Sarah Snook (Shiv Roy) won an Olivier Award last month for her performance in a one-woman version of “The Picture of Dorian Gray” that is expected to transfer to New York next year. Also in London, Brian Cox (Logan Roy) is starring in a revival of “Long Day’s Journey Into Night” and J. Smith-Cameron (Gerri Kellman) is planning to star in a revival of “Juno and the Paycock” this fall.