Apple rebrand podcasts: here's what you need to update
Apple have changed their podcasting service. You need to change branding on your own website - here's how
Used to saying "get our podcast on iTunes"? Don't do it: because it's not called that any more.
New: "Apple Podcasts"
Apple have rebranded their podcasting service to be, simply, Apple Podcasts. They've produced a nice new badge for your website, marked simply Apple Podcasts. You should go and replace your badges and icons now.
Apple have sent an email to podcasters recommending ways of talking-up your podcasts. They say:
You can direct listeners to your show by saying “Listen to [Your Show] on Apple Podcasts” or “If you love this episode, share it with a friend on Apple Podcasts”.
Apple also recommend including @applepodcasts whenever you promote your podcast on Twitter. They promise to regularly retweet and promote interesting and new shows.
If you produce a lot of podcasts, you might want to consider a “provider page” - a collection of all the different shows from your station or network. Apple have more details and information about this on their website.
You might also consider that many Apple users also use other players, like Overcast.
Don't forget about Android
If your listeners have an Android phone, an Apple Podcasts link does nothing. It's a complete dead end.
At the very least, consider a link to your podcast on an app available for Android. PocketCasts or player.fm are good links to use. For listeners in the US, you can also link to Google Play Music, though that is relatively pointless in other countries.
The failsafe is also to include your RSS feed.
I don't know a "good" way to link to all of these options in decent UX, but my own podcast (subcribe!) is on Apple Podcasts, Google Play Music, PocketCasts, player.fm, other Android apps, and here's the RSS feed.
While you're there
If you're in an "updating badges and buttons" mood - check your buttons for your apps. The Google logo should not be in a serif font: if you have that, you have a logo which is well over 18 months out of date. Here's where to find a Google Play badge. Note, too, that they prefer "our app is on Google Play" not "get our app from Google Play".