On Clyp we do not have “Private” Clyps, but we do have Unlisted Clyps. An unlisted Clyp will not be searchable and will never show up on any of our lists. We respect your privacy. However, anyone you share the link with will be able to access your Clyp.
To make your Clyp Unlisted, go to your profile page and find the Clyp. Click the "Edit details" button for that particular Clyp. At the bottom of the details window you can make the Clyp unlisted. After you do, you'll notice a new longer URL in the preview. This is the link to your unlisted Clyp.