Your Dying Light: The Following - Enhanced Edition disc should add your DLC items to your game automatically. Just remember to fully download the game's critical update just after the disc's installation process.
You also need the update if you own the Dying Light Enhanced Edition base game + the Season Pass. The difference is that you are able to install the DLC items individually from the PSN Store. If you are having trouble with a DLC item, try out the following options then:
#1. Open your PS4's SETTINGS, select PSN, select RESTORE LICENSES, click OK, go to MY LIBRARY on PS4, you now get the download option for your content and the download should start.
#2. Sign in to your store.sonyentertainmentnetwork.com account and initiate the download process directly from there.