This guide will tell you where to catch the Phoenix in Hogwarts Legacy.
Phoenix is the rarest beast in the game. You will need to follow the main story until you reach the third trial. Finish the third trial and you will get the quest Prepare For Your Owls.
In between these trials, you will get the quest for Deke and the room of requirement. Just keep progressing when they pop up and the final quest that Deke will give you for the room of requirement is Phoenix Rising. You have to complete that quest to get the Phoenix.