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.
The shop at 12 Mercer Street will offer a small sliver of Gallagher’s fashion archives, with the rest available by special order.
Entertainment in recent years has included Florence + the Machine, Lady Gaga, Rihanna and Kanye West.
She has been named senior vice president and publisher of the Everyday Food and Whole Living brands.