Fawn's secret life

The new neighbour
You meet Fawn for the first time when you pay to rent condo; she lives the next door from you.

After meeting Fawn, keep talking with her every day, until she leaves you alone, then search through her apartments until you find the "Torture Rack" club's membership card.

Spying on Fawn
Visit the club and try to ask the receptionist what Fawn is doing here. They wouldn't reveal the private information, but would offer to buy that card back from you. You are free to agree or refuse, that wouldn't have any effect on the rest of the quest, though Fawn would react badly when she finds out. Either way, your only option left is to wait for Fawn until she exits the building, which wouldn't produce any result.

Go home and take some rest, then talk with Fawn again. She would reveal what she works as part-time dominatrix at this club... and offers you to become her sub.

Quest would only progress further once you accept.

Preparations
See also: Cassie's quests

While you already can do several scenes with Fawn, to progress further you must finish another quest first, in order to meet Arlene and introduce her to BDSM.

Dark side of BDSM
Try to ask Arlene about trying to be her sub. She would refuse, saying what you must ask your actual dom first. Unfortunately, Fawn would vehemently refuse, no matter what you state as your motivation, saying what she thinks what people like Arlene represent everything wrong with the BDSM culture. She would be not in the mood, so just go rest for now.

Visit Fawn again in her condo, and ask her to try and act harsh with you by herself, to see wether it's really as bad as she thinks.

Fawn would go overboard with it, forcing you to say your safe word (twice!), and once she recognises what she just did, she would freak out. Once you wake up, she wouldn't be there, neither at her condo nor in the club. Talk with Arlene, then with receptionist, to learn what she run away to her family, at the Upper New Ark.