Black Ops 3 was released early in the PS4 lifecycle. However, later updates require higher firmware. If you are on 5.05, you need a backported update PKG (patched to spoof a higher firmware). If you are on 9.00, you can install the original updates.
DLC Packs: Including Awakening, Eclipse, Descent, and Salvation. call of duty black ops 3 ps4 pkg link
Q: How much storage space do I need to install Call of Duty: Black Ops 3 on PS4? A: You will need at least 55 GB of available storage space to install the game. Black Ops 3 was released early in the PS4 lifecycle