Parts for a Kenmore Elite ice maker are available from eBay and Sears PartsDirect, as of 2015. All of the parts sold at Sears PartsDirect are new, but some of the parts sold on eBay are used or only available through auction.
When searching on the Sears PartsDirect website, a person can find the parts needed based on the model number of the ice maker. Finding the right part on eBay can be a bit more tricky, though most sellers list the part number in the listing. Searching eBay for the part number or ice maker model number is a good place to start.