Although the Salvation DLC pack has been up for download on PlayStation 4 in some regions since yesterday, it isn’t playable until you download the latest Call of Duty: Black Ops 3 update (1.15/1.16), which is now available on PS4 on Xbox One. According to reports, the PS4 update is 1.5GB, while the Xbox One update is 2.5GB.
Here’s the full list of patch notes for the update on PS4:

Global

Salvation DLC 4 Map Pack Support

Multiplayer

General

Addressed an issue where a user would occasionally lose menu functionality upon joining a game.
Addressed a lobby issue when all members of a party did not have the same maps. 
Switching a lobby to a CWL game mode no longer displays debug text. 
Addressed an issue that caused overlapping text during the Ban/Protect phase of a CWL match.   New Emblem and Calling Card breadcrumbs are now behaving properly. 
After unlocking all Calling Cards in a Black Market set, the Featured Card will now be properly animated. 

In-Game Store:
CWL Champions Pack:

CWL Champions Pack is now available to purchase for 200 COD points.
Contains a unique CWL themed weapon camo.

CWL Team Packs:

CWL Team Packs are now available to purchase for 500 COD points.
Each Package contains a Calling Card and Camo for each team in that region.
ANZ: Excellence, nV, Orbit GG, Tainted Minds, Mindfreak
EU: Team Infused, Millennium, Splyce, Epsilon, Supremacy, LDLC
NA: Optic Gaming, Faze Clan, Rise Nation, Team Envy, Team Elevate, Cloud9

Black Market...