She was curator of Asian art and then director of the Yale University Art Gallery. At Yale, she contributed to the development of the Association of Art Museum Directors (AAMD) guideline discouraging the sale of artwork in a Museum's collection, even to cover operating costs. In a brief, she detailed her view that museum collections are "a public trust". She has also lobbied the U.S. and Chinese negotiators to ensure that implementation of UNESCO rules about non-archaeological cultural exports do not tie the hands of American curators.
She came to Seattle in 1994 to head the museum, and in her tenure, has added over 2500 works to the collections. Among these are many Asian art treasures and works by Van Dyck, Bierstadt, Richard Serra and Alexander Calder. The museum has also established a sculpture park. The museum's endowment has tripled to over $75 million and the region's first conservation studio was opened.. The museum was embarrassed when a Matisse painting in its possession was proven to have been looted by Nazis and legitimately owned by a French Jewish family, and Gates brokered an 11th hour settlement that returned the artwork, after which the museum sued the gallery which had sold it the painting in the 1950s. Gates has co-authored Porcelain Stories: From China to Europe and Biblical Art and the Asian Imagination