ADD Private browsing!!!!
are you kidding me
Hello there, and welcome to Vivaldi.
This has been discussed on the forums before, and it seems to be a fairly popular feature request. The most popular feature requests are the ones most likely to be added to Vivaldi. In the mean time, do note that the browser is still in development, and has not even entered an alpha state yet.
To quote the homepage of Vivaldi, "It is a build intended to show the direction of our product. It is not perfect, far from it. Some of the key features we integrate are yet to be implemented, optimization needs to be done. But we hope that you get a glimpse of our product and what you can expect from us."
Also, here are a couple of threads discussing private browsing in Vivaldi: