"I got an usb install stick with high sierra.
Is it possible to do a clean new installation of high sierra on a MacBook Pro 7,1? (2,4Ghz, 4GB RAM)"
You might be able to do it.
But... I wouldn't recommend it unless you upgrade the RAM and drive first.
You'll ABSOLUTELY need an SSD "in there" unless you can be happy with a computer that runs... well.... s_l_o_w_l_y.
Is that what you want?
And 4gb of RAM is going to make matters worse, because the OS will be hitting the drive with page-ins and page-outs, putting even more demand on a platter-based hard drive.
I'd recommend that you upgrade the drive and RAM anyway.
This doesn't have to be an expensive proposition.
Get the cheapest SSD you can find, either 250gb or 500gb.
Get ONE 8gb RAM DIMM, and replace ONLY the topmost DIMM (with the back off).
That will give you 10gb of installed RAM, enough for any Mac OS.
If it was me, I'd upgrade to, say, El Capitan (a very good version of the OS) and just "leave it there" for the remainder of the life of the MBP...