If I create a tkinter.Label with parameter fg = PRIMARY_COLOR and than .pack() it, if I change the value of PRIMARY_COLOR variable, call the .update() method of the widget, foreground color will not change. I know, why this is happening, but can I somehow do, that the widget will change foreground color with the PRIMARY_COLOR variable change? Can I make some kind of "pointer"?
No, you cannot do what you want. You will need to call the configure method of every widget that uses that color.
Update tkinter widget parameters with "pointer"