Sorry, I should have noted that we are on PE 2018.1.0.261. Thanks!
My experience is that you can not move the tabs. You'll have to delete the existing tabs to the point where you want to insert the new tab then recreate the tabs you deleted. Be careful not to delete the existing data sources so that you'll have them available later in the rebuilding process.
Another alternative might be to create sub tabs at the location you want to insert the new dashboard view. This may allow you to only disturb part of your existing dashboard.
A best practice that that I use is to clone the existing dashboard then make all of your changes on the cloned copy. Once all is working properly you can put the new dashboard into production. This method allows you to keep the original for reference purposes.
Thanks for that info! I did have to delete the last two tabs and recreate them in the order I needed. Not too much of a hassle but it would be helpful if we had the ability to change the order!