His professional career began in the television film The 10 Million Dollar Getaway (1991) as John Murray.
Over the next eight years, Klace appeared in several other television series, such as Beverly Hills, 90210 (1996), Seinfeld (1998) and 3rd Rock from the Sun (1998), as well as a few films, including Money for Nothing (1993), Heavy Gear (1997), and Roommates (1995).
His most notable appearance came in the final episode of Seinfeld, where he played the jailer of the four main characters.
He began using the spelling Klace in 1999 when he played Dremk in an episode of Star Trek: Voyager, and Fox in the film Wishmaster 2: Evil Never Dies.
He then went on to perform other small roles in television shows and direct to video films, including American Tragedy (2002), The Guardian (2002), Charmed (2003), 24 (2003), ER (2004), NYPD Blue (2004), and Malcolm in the Middle (2006).