OK... I know everyone is having problems with this so I will tell you what I did.
First go to https://store.sonyentertainmentnetwork.com and login. Re-download the DLC and add it to the Queue; it will not actually do another download on your PS4.
Second go to your PS4 and under the PSN settings hit "Restore Licenses". If you have the expansion pack it will set the time on it to 0:00:00 because the DLC is not out yet.
Third g to the Tower and visit "special orders"; she will have a new emblem called "VANGUARD HONOR". I equipped it just incase.
Last... Go to Van guard Quartermaster in the Hangar. You will purchase the items but they are cheap!
GOOD LUCK
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Which DLC? The Digital Guardian Edition? I can only find the Vanguard Armoury for my PS3, and when I click on it in the download list it takes me to the Digital Guardian Edition... which the PS4 rightfully claims is already installed... I'm maybe thinking those using the PS3->PS4 upgrade didn't get the Vanguard upgraded?