need logic gate output higher than vcc
One way you could go about it is by using a logic level MOSFET. It is called logic level because you can fully turn it on (as in turn on a switch) with logic levels (~ 4.5 to 5V) at its gate. 







simulate this circuit &ndash; Schematic created using CircuitLab

So what this does is the following: When there is 5 volts at the output of the NOT gate, that voltage will turn the MOSFET on since it is working as a switch here. Turning on the MOSFET means that there is a conducting path between the source and drain terminals and therefore the buzzer circuit is now complete (It will sound). When there is 0 volts coming from the NOT gate, then the MOSFET will be off and the buzzer won't have a ground connection and hence won't sound.

The 10K resistor has to do with some of the characteristics of the MOSFET such as large input impedance and capacitance. It just ensures that the MOSFET won't stay on after you once turned it on or will randomly turn on by means of static charges etc. 

Since it is an intro course, this may be out of the scope but that is how these issues are typically addressed. Hope it helps!