Born in Western Australia, Australia, Klensch moved first to Sydney, and then overseas to London and Hong Kong before settling in the United States. She worked as an editor at Women's Wear Daily, Vogue, W and Harper's Bazaar before joining CNN in New York City on its 1980 launch.

She received awards for her CNN coverage from the Council of Fashion Designers of America, the Fashion Group International and the Anti-Defamation League. The Italian government presented her with the Italian Order of Merit, the Ordine al Merito della Repubblica Italiana for her reporting on Italian fashion and design.

She appeared as herself in several television shows and films, including Robert Altman's Prêt-à-Porter (1994).

Klensch has written a series of a fashion industry-oriented murder mystery novels, featuring the character Sonya Iverson.

• Live at 10:00, Dead at 10:15 (Forge, 2004)
• Shooting Script: A Sonya Iverson Novel (2006)
• Take Two (2007)

She has also written a book of practical advice on how to use fashion in finding a personal style.

• Style (Perigee Trade, 1995)