At an art fair, there are many visible roles in play: director, exhibitor, client, critic, installer. But an undersung — and increasingly critical — part is the one inhabited by the conservator Gloria Velandia and her team of trained assistants. Almost invisible, except to those in the know, Velandia runs the international circuit as the preferred conservator for major-league fairs (including Frieze New York, which begins this Thursday). “I’m the doctor on call,” Velandia says of her unique position under the fair tent...