Rack, in the context of "set of antlers," refers to the entire arrangement of antlers on a deer or similar animal. It is the branched series of bony growths that extend from the head and is characteristic of certain species of male deer.
Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: Unlikely thing off of which to buy haute couture. Explanations are generated by AI and may be inaccurate.