Pounder was born in Georgetown, British Guiana (now Guyana), daughter of Ronald Urlington Pounder and of Betsy Enid Arnella (nee James). She was educated in England and moved to the U.S. in 1970, where she attended Ithaca College.

Pounder made her acting debut in the film All That Jazz (1979).

Pounder started her professional career in New York City theater, where she appeared in The Mighty Gents, by Playwright Richard Wesley, and Open Admissions on Broadway. She moved to Los Angeles in 1982. Pounder starred in the film Bagdad Café, and has made smaller appearances in many other successful films. She has focused primarily on her television career. In the early 1980s, Pounder first appeared in guest roles on Hill Street Blues, and then on several popular shows (The Cosby Show, RoboCop 3, L.A. Law, The X-Files, Living Single, and Quantum Leap) before landing a long-running recurring role as Dr. Angela Hicks on ER, from 1994 to 1997. In the midst of this she co-starred in the Tales From the Crypt feature film Demon Knight (1995). She then returned to guest appearances on other shows, including The Practice, Law & Order: Special Victims Unit, Millennium, The West Wing (where she was considered for the role of C. J. Cregg), and the short-lived sitcom Women in Prison.

As one of the founders of Artists for a New South Africa, Pounder has energized awareness of post-apartheid and HIV/AIDS issues. In an interview, she said about the pandemic: "When it's this massive disease, and it's affecting things in five thousand different ways, it requires great strength and power—and there is power in numbers. So we need to involve as many people as we can, like we do with ANSA. I call it my little engine that could. It is a remarkable, tiny organization with a huge outreach. We use actors and artists with the biggest voices so they can use every opportunity to talk about AIDS."