Your creator may have moved their private podcast feed to a new host behind the scenes. Nothing you need to worry about, but you probably received a new invite to start listening to the same content just hosted somewhere else. Here's how to manage the new invitation to continue listening without interruption:
Subscribe to the new invitation as you've done before by choosing your preferred podcast app.
Delete your subscription to the older version of the feed.
In Apple Podcasts, you can sort your library by when you followed the show. Delete the older one.
You can of course swap those 2 steps above, but it's nice to know you have access to the new version before you start deleting stuff. The old version will eventually stop working automatically; removing it just cleans up your app.
Here's a 2-minute video showing what it looks like: