How to unlock: Receive an e-mail from Peebee [Tempest].
Here you can find the guide for Peebee: The Museum Trip quest. This is one of the side quests in Mass Effect: Andromeda game that belongs to the category called "Allies and relationships". This quest is connected with Peebee and you get it automatically after you return from a city on planet Aya (after you unlock the access to the entire planet by making progress in the main storyline). In this quest you must visit the titular museum on Aya. The most important part is the last one because during it you must decide whether you want to have a serious relationship with Peebee or not.
Unlocking the quest
After making enough progress in A Trail of Hope main quest and unlocking the full access to planet Aya (you can do this by saving Moshae Sjefa) return on Tempest. You should receive an e-mail from Peebee. Read it and you learn that she wants to meet you in the museum.
Speak with Peebee in the museum on Aya
Go back on Aya and head to the history museum where you find a completely drunk Peebee. Speak with her.
Despite the "official" ending of the quest, you must now make the most important decision about your relation with Peebee. When you go back on Tempest you can visit Peebee in rescue pod and have some fun with her in zero gravity. During this scene you can decide whether you want to simply spend some time with her or start a serious relationship with her (warning - this choice blocks the possibility of being in relationship with other characters that you were already flirting with!). If you want to choose the second option then you should select the dialog option presented in the picture above.
Rewards for finishing the quest: XP.