HBC sees Burstell engaged in bringing innovative concepts to all of its divisions.
A product and marketing executive at Yves Saint Laurent, he will take over Isabelle Guichot's role.
Raf Simons, Christian Louboutin, Marco Zanini and a host of other designers attended.
The vote at the annual general meeting Friday is non-binding.
Known as Stacey G, she is among the most in-demand spin instructors at the New York studio, and getting in to her classes is tough.
Many brands showcasing their wares during Paris Couture Week conjured the spirit of the Roaring Twenties.