it's quite a simple thing to do on windows 10, on windows 7 i'm sorry to say it doesn't fully support it
I don't think that Windows 7 "lacks" 4K support - rather, it doesn't support HiDPI displays and text scaling all that well, compared to Windows 10.
I was able to get VSR running on my 1920x1080P monitor, at a resolution of 2560x1440, just fine in Windows 7. But I had 1:1 scaling, so icons and text got tiny. (Which is fine with me.)
When I upgraded to Win10, and enabled VSR, it automagically tried to enable 1.25X text/icon scaling. Which, honestly, made it look not much different than 1920x1080P res, only the icons were "bulkier". I had to manually crank the scaling back down to 1:1, to get the desired effect.
from what i can remember and fine online etc, to a degree you may make it slightly better, but no it won't be how it is on windows 10, which fully supports 4k out of the box and most of the time auto alters / scales the windows to fit the display.
the issue for me is your trying to couple the latest display technology while trying to hold on to a old version of windows, while it works, it doesn't or won't be able to re scale to a size which wasn't even in the planning on the time frame the older version of windows 7 was being tested, same goes for putting in the latest display card, it may fit your board, but the drivers may cause some issues with an older version of windows also