Anne Hawley, director of the Isabella Stewart Gardner Museum, sits in her new office as workers install finishing touches on the museum’s new wing, which opens to the public Jan. 19. Designed by Renzo Piano, the $114 expansion more than doubles the Gardner’s footprint. For Hawley, the project exemplifies her long-term approach: It demanded patience, suggestions from multiple sources, reams of documents, and numerous hearings. And it required her to weather some criticism as the museum made the case that moving ancillary activities into a new building would actually help preserve the 108-year-old palace built by Isabella Stewart Gardner.