Rex is a Coelurosauravus who came through an anomaly from the Permian Era into the Forest of Dean. He was discovered by a young boy, Ben Trent, who thought he was a rare species of lizard. Ben's mum contacted Wellington Zoo to see if they could rehome Rex, and Abby Maitland arrived to collect him. Abby had never seen a lizard like Rex and asked Ben to show her where he was found. While in the forest, Abby met up with Cutter and his team and discovered an anomaly to the Permian Era, it was then they realised Rex was a Coelurosauravus. Cutter ordered all creatures that came through the anomaly be sent back to their own time, but Rex sneaked back through to the present day and Abby adopted him - at first without Cutter's knowledge.
In series 2, Rex was kidnapped by Connor's ex-girlfriend (Caroline Steel) and taken to Oliver Leek's menagerie. Although injured, he escaped with Caroline's help before the collection destroyed itself.
When Abby and Connor became lost in the Cretaceous Era, Rex was taken to live at the ARC. It appears that he's continued to live there even after Abby returned home.