Bloodborne The Old Hunters DLC Installed but item isn't appearing
I got the exact same problem. Look on the disk box for the region code. Mine states "Region ALL" (instead of Region 2) but I got the DLC for Region 2. Thus, it will not play.
☹ Welcome to the horrid world of DRM…
Note that as a gesture of good will, Sony refunded me. However, I would not expect this to be a common occurrence thus do check regions before buying!
I'm not sure at what point in the story you get to access the content, but I'm pretty sure the actual data was downloaded and installed in the 9gb patch a few days ago. Once you "have" the DLC (purchased it on PSN), you'll just have to get to the appropriate place in the story and fulfill whatever criteria is necessary.
Also see this question for more information. (Duplicate?)