In 2002, the economy and finance minister, Francis Mer, refused to nominate her to lead the DREE, saying: Clara, vous avez neuf enfants, un mari qui fait de la politique.

[14] Gaymard's style of management was cited as being liberal and progressive, notably her work for the LGBT community; as she supported the development of the diversity organisation, called GLBTA (Gay, Lesbian, Bisexual and Transgenre Alliance).

[17] In 2016 Gaymard co-founded the investment fund and philanthropic group Raise,[18] with French businessman Gonzague de Blignières.

[19] Parallel to her career, Gaymard was a lecturer in contract and public law, an auditor of the 53rd session of the Institut des hautes études de Défense nationale,[20] and a founding member of the Jérôme Lejeune Foundation.

Gaymard is the daughter of Professor Jérôme Lejeune, the doctor and geneticist who discovered the chromosomal link of Down Syndrome, and Birthe Bringsted.