Several things that could be the problem:
1. The DLC and your physical copy region is different, and the game couldn't detect it. This is a common problem, since there's several DLC that were region specific, although it has the same language (i.e English).
To solve this, try playing it on the ID that you used to bought the DLC.
2. The PSN ID that you use to bought the DLC hasn't been set to primary, and you played on a different PSN ID.
To solve this, make all of your ID on your system to primary. It's in the Settings>Account Management>Activate as your Primary PS4.
3. The game hasn't been updated yet, hence it couldn't install the DLC.
4. The game/DLC license has expired. Try to restore it trough Settings>Account Management>Restore Licenses.
If all of those wasn't avail, then you must contact the PS Customer Service and ask them for a resolution.