No, you do not need to pay for Sotheby's brokerage service for Private Sales. 

Sotheby's Private Sales service is designed to provide a bespoke buying and selling experience for clients looking for discretion, privacy, and personalized service. With Private Sales, you have access to a curated selection of artworks, objects, and luxury items that are not available in public auctions. Sotheby's specialists work closely with you to identify items that match your specific interests and needs and then handle all aspects of the transaction, including negotiating prices, handling payment and shipping, and providing guidance on any necessary customs and import regulations. There are no additional fees charged by Sotheby's for this service, although you may be responsible for any taxes or other fees associated with the purchase depending on the item and your location. Overall, Sotheby's Private Sales service offers a unique and convenient way to acquire or sell exceptional items with the guidance and expertise of Sotheby's specialists.

You can find items currently available for private sale here.