Hi,
ive recently come to the conundrum that i need more space on my playstation, but im way to hesitant to do anything before knowing how it will impact my progress, DLC content (purchased both expansions), and my gear..
Your character data is saved on Bungie's servers and linked to your PSN ID/gamertag. One you get Destiny installed and patched on the new hard drive, just sign in with the same PSN ID and your character's will be there.
I don't have a PS4, so I'm not sure if swapping the hard drive does anything with the licenses. If you have any trouble downloading DLC's, try restoring licenses once you get the new hard drive setup: https://www.bungie.net/en/Help/Article/12181