She was born in Georgetown, British Guiana (now Guyana) and was educated in England. She moved to the U.S. in 1970, where she attended Ithaca College.
Pounder started her professional career in New York City, 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.
From 2002 to 2008, she starred as Detective Claudette Wyms in the FX police drama The Shield. For this role she was nominated for the Primetime Emmy Award for Outstanding Supporting Actress in a Drama Series in 2005 and an NAACP Image Award.