I just upgraded to MacOS Sierra and I lost a week-long of notes in Notes. It happened, after I restored a backup from a week ago and then installed Sierra. All my notes sync with iCloud, but there simply aren't any notes now from since last week. Is there any kind of way to recover those notes, because they are reaaaaaally important to me... Thanks:)
No. They are gone. iCloud, for a lack of a better word is a "sync conduit" between your devices; it's not a backup. This means that a change you make on any of your devices is what gets synced.
When you restored the 1 week old backup from Time Machine, more than likely, Notes did a sync which overwrote what was on iCloud because it "assumed" that was the latest data to be synced.
What you should do in the future....prior to upgrading your OS do a manual Time Machine backup so it saves the latest state. This way you know for a fact that what you restore is your most recent version.