As soon as the park investors consider that you are able to build new enclosures, a list of objectives will appear on the right side of the screen. Meet all the achievements to unlock the new habitat, and you will be able to host different species! A small exclamation mark will appear over the quest widget every time you complete a task. Tap on the widget to claim the rewards. 
Once you complete 100% of the objectives, you can build the new habitat!  Don't worry if you can't see a new task list. That means that you have unlocked all the habitats available so far. The team is actively working on more content updates, and new task lists will show up as soon as they are released.