Normally render printed on paper looks darker than it was on screen. What is the most correct way to solve that? To provide some extra exposure when rendering or just to rise the already rendered image brightness say in Gimp? Or anything else?
Don’t think that is a problem to be solved by rendering. You need to have both your screen and printer calibrated correctly.
Yes you are right, that would be the best. But I less likely to expect them calibrated. So I need some alternative.
Sure, not everyone has the luxury that 
But there should be ways to calibrate your hardware better yourself. It depends on OS / drivers how to do that.
If there is no other way, you have to do it for each viewer / image editor application separately (if possible it all). In Blender, in the scene tab -> color management, you can mess with exposure and gamma for the internal viewer, which might give you what you want.
Yes that luxury is not for everyone and that’s my case:) Thank you. You know I use only Gimp for editing, so it won’t be difficult to tweak an image in it. My concern is just about how not to distort the initial picture dramatically. Both the editor and extra exposure with gamma would affect it, I just wanted to understand in which way I would get lesser distortion. From your answer, I see that I could try both ways - internal and external means as well. Thank you very much for the answer.
Also, look out for the filmic color mode. Filmic tries really hard to never ever burn out bright areas, which means it’s really hard to get real white, which when you are printing out, white is pretty important.
Just something to consider.
SterlingRoth thank you very much for the point. Yes I use Filmic and I’ll pay attention to it.
This is normally referred to in the printing trade as "pre-flighting."
The image presented by the client is normally an RGB image, hopefully but not necessarily prepared on a calibrated monitor, which must now be rendered on a particular paper-stock with a particular printing process.
“Consumer-grade printers” (and even “pro-sumer grade”) will perform a built-in approximation of this process, “good enough for peace work” as my grandpa used to say, but nowhere like the real deal.