In which of these TV shows did the chef Gordon Ramsay not appear?

The answer is Auction Hunters because this show does not feature Chef Gordon Ramsay. Auction Hunters is a reality television series that follows two people who buy storage units at auctions and then resell the items they find inside. Gordon Ramsay is a world-renowned chef who is notably known for his appearances on cooking-related shows such as Hell's Kitchen, Kitchen Nightmares, and MasterChef.