Only gym administrators can make a new exercise. We have to limit the number of people who are allowed to do this because otherwise we end up with 10 copies of the same movement with different names. As a regular user you'll be able to use our exercise suggestion form to suggest one for us to add.
If you are a gym admin you can create a new exercise via the Movements page. Go to the "explore" menu in the header and click on the "movements" link from the drop-down that appears.