Flip a Schmitt-Trigger when current flows through a Zener diode
The first circuit can be made with a bit more "steep" respose by using an NPN instead of an NMOS:







simulate this circuit &ndash; Schematic created using CircuitLab

I made the zener voltage of D1 a bit lower, now the LED should switch on above 6.2 V + 0.7 V = 6.9 V.

Regarding the circuit with the Schmitt trigger, note that the levels of the Schmitt trigger are relative to the supply voltage so it is chasing a moving target (the trigger level moves up as the supply goes up). 

If you could the Schmitt trigger's input to ground then that stays constant as the trigger level changes with the supply. This might work, what zener value you need I do not know, I would experiment a little. To make the LED light up when the supply (and trigger level) is larger than a certain value, 2 NAND gates in series are needed. If you reference the LED from ground then one NAND gate will do of course:







simulate this circuit

Am opamp based solution could look like this:







simulate this circuit

R7 is optional it adds a bit of hysteresis like in the Schmitt triggers. Make R7 smaller to increase the distance between the trigger levels. Remove R7 to have no hysteresis at all.