Claire Gibault began her career at the Opéra National de Lyon before becoming the first woman to conduct the Filarmonica della Scala and the Berlin Philharmonic. She was made an Officer of the Legion of Honour by the French government in 2016. In September 2017 the French Minister of Culture awarded her the title of Commander of the Arts and Letters.

She was music director of Musica per Roma from 2000 to 2002. She was assistant to Claudio Abbado at Milan's La Scala, Vienna's Staatsoper and London's Royal Opera House Covent Garden. In 2004 she helped him found the Orchestra Mozart di Bologna.

Over the years Claire Gibault has been invited to conduct opera and orchestral works for prestigious institutions such as London's Royal Opera House, Washington Opera, Opéra Comique and Philharmonie de Paris, the Opéra de Marseille. A passionate advocate of contemporary music, she regularly collaborates with leading composers and has been invited to conduct world premieres ranging from symphonic works to opera.

In 2011, inspired by her experience with Claudio Abbado, Claire Gibault formed the Paris Mozart Orchestra, giving some thirty performances with her musicians each season.