When you purchase a premium theme on Tumblr, you get one license for that theme on the blog you specify when you purchase a theme. If you want to use the same premium theme on a different blog, you’ll have to purchase it again.

You can find out more about the theme license in Tumblr's Terms of Service - check out sections 9 (Themes) and 10 (Paid Services). If you have any questions, it's best to contact Tumblr directly for help with this. You can contact them via the Help section.