@czarbucks
Yes and no. You can't move the button as such, but you can create a new button.

To do that, create a new Command Chain with "New Tab" as the only command, if you want, add a custom icon and add the button to the Address Bar.
Check the following tips for step by step instructions:
- https://vivaldi.com/blog/tips/tip-123/
- https://vivaldi.com/blog/tips/tip-594/

You can also check out our Modifications forum on https://forum.vivaldi.net/category/52/modifications for ways to customize the browser if somehow there isn't a setting for what you want yet. 😉