Professor Herik from the Nexus tech labs has asked you to make a home for a young pyjak aboard the Tempest. This mission is only available in the Deluxe and Super Deluxe editions of Mass Effect: Andromeda.
Once you have access to the Tempest, read your emails to find one from Professor Herik. Acknowledging the email will add the mission to your journal.
After reading the email from Professor Herik, travel to the Nexus Docking Bay and investigate the northern corner near the general merchant. You will find a container labeled "Pyjak"; examine it to progress.
When you return to the Tempest, the pyjak will already have escaped from its cage. Find and interact with it to complete the mission. It can thereafter be found in various locations around the ship, and each interaction will trigger dialogue from one of the crew members.