In order to set episodes for Supporters only, visit the Episode Info section of your episode and change its visibility to Limited Access.

You can set also the entire show to Limited Access. Visit the Podcast Settings and change your podcast visibility to Limited Access. Listeners will need to become a supporter to be able to listen to your podcast.

Give your supporters access to the most recent episodes before they are published on your public feed.

Then you can change their visibility to Public after a few days.

And don't forget to promote your link, take a look here for some tips!