Hello,There is no known fix (or cause) for the bug. If it occurs, the only option is to reload a save and try to begin the quest again. If it simply refuses to work, you are still able to play by "beginning a new game" for HoS content only. Alternatively, you'll need to start a whole new playthrough of the main game.
There's no guarantee that any of the following suggestions will work, but based on other issues, it may affect the likelihood of the bug appearing:
1.) Limit any background processes (marketplace, background updates / downloads, chat / friends features, streaming, etc.) on the PS4. Disable all of it and play offline. Free up as many resources as possible on your console.
2.) Do not try to start the quest very late into a playthrough. The longer you have been playing the same game (saving and reloading the same paythrough), the more of a chance things have of borking. There is a similar concern for NG+ mode and very high levels. The game was designed to be played through to a conclusion; it was not designed for a single playthrough to be played "indefinitely".
3.) Manage your inventory before beginning the quest. Dump every single thing you don't absolutely need into a stash or sell it. Having a very loaded inventory can create issues after a while due to how the game saves items and keeps track of them. This is especially true if you have multiple "copies" of weapons or armor in your actual, carried inventory. (Meaning, for example, numerous "Velen Longswords" -- especially if they have been in your inventory for a long while.)
4.) If the game has been running for a time when you're about to start the quest, exit, restart your console, and reload the game fresh, then start it. Again, ensuring the game has a lot of resources available may help.
5.) Don't fast-travel once you start the quest. (At least, not until you get passed the part that's bugging out.) Also, don't take any "shortcuts" to save time (hopping over mountains to avoid traveling around, etc.) Just follow the path the game sets out for you and ensure you interact with all the stuff on the way.
To date, as far as I know, there is no known reason for the bug to be happening. Why it affects certain people and not others is a complete mystery. All attempted fixes have worked for some people...then it would simply crop up again for others. Everything that can be done has been done.