Around the time she was in the seventh grade, South African actor Thando Thabethe auditioned for the lead role in a school play. It didn’t pan out the way she’d planned — she landed a small part in the choir, “sort of singing ‘Kumbaya’ and not really doing much,” she recalls, with a laugh — but a spark was lit. “Even just being part of something that small at such a young age is what shaped me, knowing that this is something that I want to do for the rest of my life.”

That life-long dream now has Thabethe poised for breakout success. First comes a star turn as Constable Nandi Cele in the crime drama “Reyka,” an eight-part series produced by Serena Cullen Prods. and Quizzical Pictures for the South African pay-tv channel M-Net that Fremantle is distributing globally. That will be followed by a lead role in “Blood Psalms,...