Not sure about the details, but I guess you need to go the brothel route, set her up as the new brothel manager after defeating the demoness, then send Sarah and Anne to her room, effectively making Priapra their mistress. Then I guess you can recruit her.
Me, I can't seem to make Priapra go to the goblins and unlock the new scenes. I give her wine and tell her goblins "fuck good", then when she wants to send someone over to screw the goblins, I tell her "why not you", making her go "ok, but don't tell anyone". Then nothing. She just sits there. The dialogue hints that I have to wait, and that she'll go to the goblins after a while, but nothing happens. She just sit there, and never appears in the goblin slums. I can't go pass the time by sleeping, because the party event is still active and effectively blocks the path to the bedroom, but even if I use the Fixer key item to pass through the walls, then sleep normally, nothing happens. I guess an X amount of erronous and unfinished events conflict with each other, cancelling any further progress at this time, but if I've missed something crucial, and someone knows, then please tell me.