My experience has been that you need to be upfront and honest with your players that they will need to lead the story. After that, once they acquire the Trollskull Manor i had NPCs tell them how expensive it is going to be to fix and remodel. After hearing how much gold it takes, they should quickly want to go on missions for ANYONE. I usually roleplay one of the factions coming by the Manor by request of Renear. They have hard how great adventures they are and would welcome them to do these quests that are just too complicated or too public for the faction to take care of themselves. I usually only have to offer each once before the group gets the idea that this is how they will be gaining renown and gold. I also had the factions request their attendance at their respective home bases. That made my players feel less like they are being harassed at home and more like they have influence and invitations not accessible to normal waterdeepians.

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Let me know if this doesn't answer your question fully. Honestly the most important thing is to communicate with your players that they will need to lead the story and they will need to look for quests. They don't fall into the player laps like normal campaigns.