Only gym administrators can make a new Movement, which can only be added via the web. We limit the number of people who are allowed to create Movements to avoid duplicate Movements created under different names.
If you are a gym admin, you can create a new Movement via the Movements page. Go to the "explore" menu in the header and click on the "Movements" link from the drop-down that appears, scroll down to find "Add a Movement" under the pie chart.
We are hard at work on a function that will allow regular users to suggest Movements for us to add. We will have this added ASAP :)