DLC content and save data is not going to work if your Dying Light physical disc is from a different region to the one assigned to the original disc you owned before and to your PSN account. The DLC will download, but then appear as "waiting for install", not allowing you to actually install it.
For instance, if your disc has the US region code, but you have used a DLC code on a UK PSN account, or you have purchased the Season Pass at Playstation Store UK, those DLCs will simply not work.
In order to verify which region code your disc has, check its "CUSA" number against the following list:
Dying Light Enhanced Edition JP - CUSA-04298
Dying Light Enhanced Edition EU - CUSA-03991
Dying Light Enhanced Edition BR - CUSA-03977
Dying Light Enhanced Edition US - CUSA-03946
Dying Light EU-2 - CUSA-02010
Dying Light JP - CUSA-01090
Dying Light BR - CUSA-01473
Dying Light EU - CUSA-00050
Dying Light US - CUSA-00078