Drop shipping, where you fulfil orders directly from a wholesale supplier, is allowed on eBay. Remember though, if you use drop shipping, you're still responsible for the safe delivery of the item within the time frame you stated in your listing, and the buyer's overall satisfaction with their purchase.
However, listing an item on eBay and then purchasing the item from another retailer or marketplace that ships directly to your customer is not allowed on eBay. Activity that doesn't follow eBay policy could result in a range of actions including for example: administratively ending or cancelling listings, hiding or demoting all listings from search results, lowering seller rating, buying or selling restrictions, loss of buyer or seller protections, and account suspension. All fees paid or payable in relation to listings or accounts on which we take any action will not be refunded or otherwise credited to your account.