I had the same issue but with Xbox and the way I fixed it (while talking to Xbox Support) was going directly to the Xbox Live Download Store and re-installing the add-on content (for free) on my new system. Maybe you can do the same with the Playstation Store. Hope this helps you and any others that might stumble upon this post!
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So I went to PSN Support and got stone walled, they couldn't help me and told me to contact Bungie but I wouldn't know how to do that
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Unfortunately I can't re download it on my psn account for some reason it's unavailable so idk what to do
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I'd try contacting Playstation support then. Xbox support helped me figure out my issue
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Alright thx I jus need to find out where the support is now
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PSN live chat, available 5am to midnight at the link posted. Tell them you purchased content on ps3, that is supposed to be available for ps4 and not showing up.
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I did that they said it wasn't their issue and that I have to talk to bungie about it