I was definitely having this problem too. I tried several suggestions made here, but I'm unwilling to log out of iCloud and have it delete everything in iCloud and start again. That would take a huge amount of time and I'm not sure it would completely solve the problem. (Would I have to do that again and again?) In my case, I discovered that the problem probably wasn't that the process wasn't happening, but rather that it was just incredibly slow. The new files that I was adding which didn't seem to be uploading were video files, typically 3 to 5 MB. One thing I tried to kickstart the process was to log into iCloud in Safari, navigate to the folder where uploads should be landing, then navigate to the corresponding folder in the Finder and drag a file from Finder to the Safari window. That certainly seemed to start the upload process, but now I'm not sure that it wasn't already going.
The next thing I did was to go to a Finder window and scroll down the sidebar to iCloud Drive. (I should have done this first.) I could see the (almost empty) progress wheel indicating that uploading was happening. By clicking the info button, I could see that 4 files were being uploaded and that a tiny fraction of the 12 MB had already made it to iCloud. The fact that the number didn't change quickly made me wonder if it was stalled, but by being patient I could see that it was slowly moving. It took more than an hour, but eventually all the files went up. Unfortunately I can't know if my "kickstart" helped or if it was already happening and I just didn't notice.
Of course, that upload speed is not acceptable!
So the next thing I tried was the terminal commands suggested by b1connected. Changing the priority of the upload process seemed like a hopeful avenue. I'm not a frequent Terminal user, so when I had trouble entering my password (there's no blinking cursor and no indication that it's even taking your input until you hit enter) I stopped and decided maybe I should log in as root. I realized that I had never enabled the root user on this machine, so I went into system preferences and did that. (Apple gives clear instructions on how to do this. You can look it up.) Then I logged out of my Mac (NOT out of iCloud), and logged back in as the root user. Now I could use Terminal and it would take my commands without a password. But after running Terminal, I realize that my desktop wasn't there and I didn't even know how to find my notes on how to do the Terminal process recommended by b1connected.
Ok, not worth it. I logged out of root and logged back in as myself.
Just on a whim, I went to one of my desktop folders and duplicated a 2 megabyte file. In seconds, it uploaded to iCloud!!!
It makes no sense to me that simply logging out, logging in as root, logging out, and logging in as me should work, but it seems like it did. I have no idea if this will last. Maybe the problem will come back tomorrow.
I did go ahead and do the Terminal procedure recommended by b1connected. Why not?