Note: Once you've completed the steps in this help doc to redirect your feed, you can start uploading new episodes to your Omny Studio account to update your feed.
Once you've imported your podcast to Omny Studio, you can easily migrate to Omny Studio without losing your existing subscribers. All you need to do is tell Apple Podcasts and the other podcast directories and apps to pull from your new RSS feeds. This is done by applying a re-direct from your old feed to your new feed.
Migrating from Simplecast
Under your Podcast Settings in your dashboard, you'll see a dropdown button for "Advanced Options." After you migrated to another service, paste your new RSS feed URL to properly redirect to your new podcast host.
After you have completed this step your feed will now redirect your feed to Omny Studio.
Note: Although iTunes will normally pick up on changes within a few days, you should leave the old feed in place for a few weeks to ensure all subscribers are moved across.