There are various synonyms for the phrase "at the close of," which means towards the end or at the conclusion of something. Some possible alternatives include "when the end arrives," "when it draws to a close," "as the final moments approach," "at the end of the day," "when everything winds down," "in the final stages," "as things come to a finish," "upon its completion," and "as the curtain falls." These phrases can be used in various contexts, such as in writing about the end of a project, the conclusion of a story, or the final moments of an event.