AMC has launched an official app for the Apple TV. With the app, you can watch episodes of Better Call Saul, The Walking Dead, and more on demand. You will need to log in with your cable account in order to watch most full episodes, though in some cases, particularly with Fear the Walking Dead and The Night Manager, you can watch certain episodes for free.
You can track which episodes you've already watched, and pick up where you left off. Full episodes will be available during the season in which they air, while AMC says that the extra features, including behind-the-scenes clips and interviews, will always be available.
You can download the AMC app for Apple TV for free from the set-top box's App Store.