Leftover prime rib can be kept safely for 3-4 days in the refrigerator stored in an airtight container. Leftovers can be frozen but I don't recommend it. Try to purchase the size that your family can consume and factor in the number of servings of leftovers that you would like for sandwiches as the meat is best the next day for this recipe. Reheating is always risky in changing the flavor and texture.