Peebee has asked you to meet her at the museum on Aya.
Acknowledge a mail titled "Ay--ay--Aya!" from Peebee. This email is received after meeting Peebee in her Nexus apartment during Peebee: Secret Project.
Talk with Peebee at the museum on AyaEdit
She is wobbling around in the museum, evidently drunk. She expresses frustration at how the angara have already done extensive research on the Remnant, and admits that she's been feeling off ever since she moved out of the Nexus.
When you return to the Tempest, Suvi lets you know that Peebee wants to speak with you. Peebee seems stressed out, and says that she always used a zero-G chamber or similar before to relax. SAM suggests turning gravity off in the escape pod, and Peebee invites Ryder for the experience. The two enjoy a few moments drifting.
She then offers you a chance to "blow off steam" together - no strings attached. Your other romantic partner doesn't need to know. Accepting the offer will further a romance with Peebee.
None (except advancing the relationship).