1. Create an Apple ID (if you don't have one already)
2. Login to Apple Podcasts Connect
3. Scroll down to the footer and select 'contact us'
4. Choose topic 'other' and mention at least the following in the message:
- Your Apple Podcasts show URL
- The podcast's RSS feed
- Your Apple Account ID (with which you want to claim ownership). You can find this under 'Details pane' in the Account section.
And indicate that you want to claim the podcast.
After 1 or 2 days, Apple will send you an email containing an authorization code, which you must place in your RSS feed (in the keyword's or copyright field). You cannot do this yourself, but you can ask your current host.
When you receive confirmation from the host that the code has been placed, you can email Apple back with notification that the code has been posted to the RSS feed.
After Apple confirms that ownership has been claimed, the podcast show will automatically appear in your Apple Podcasts Connect account.