Please ensure that you have the Season Pass file installed to your Xbox One before starting the game. To check if this is installed, please sign into your Xbox profile on your console and ensure you have a strong connection to Xbox Live and that all Xbox services are live.
Next, highlight The Walking Dead: A New Frontier tile from the Xbox dashboard, press the Menu button on your controller, and select Manage Game. If the Season Pass file is listed in the Ready to Install list, please select this to install the file. You'll be able download episodes normally in-game once this installs.
If you don't see a Season Pass file anywhere, please uninstall the game, then hard reset your console by holding the power button down for 10 seconds. This will clear the cache. Restart your console, reinstall the game, then launch it again and see if you are now able to download episodes.