If you are a holder of a TeamViewer subcription, you can use TeamViewer 13 without an additional purchase. If you are having a TeamViewer perpetual license for TeamViewer 12, you can order an update.
The easiest way to find out, is to open your TeamViewer application and login with your TeamViewer account. When logged in, click on Extras --> Checkfor license updates. If the shop offers you "just" additional channels, your license is ready for TeamViewer 13. If it offers you an update to TeamViewer 13, you can order the update directly.