To release a dinosaur, your pen needs to be filled with dinosaurs of each level (1 to 6). Only then can you release a 6th level dinosaur. Once your pen is full, tap on the label with the name of the dinosaurs and then tap on “Release.”
Be aware that it will reduce your popularity index a bit. In exchange, you will get Gems and a Totem.
It’s possible to have up to three Totems. Totems provide a parameters boost during Arena Battles.