Can I use a Zener diode in place of a 3.3V voltage regulator to power an nRF24L01?
There are two ways that you can use a Zener in your circuit.  Neither is all that good.
First, there's the standard &quot;shunt regulator&quot; circuit.
It looks like this:



simulate this circuit &ndash; Schematic created using CircuitLab
You have to size R1 to provide the full current to the nRF24L01 at 3.3V.  That's about 14 milliamperes.
That also means that your circuit will always consume 14 mA - even when the nRF24L01 is sleeping.
If you can assume that the 6V will never go above 6.6V, then you could do the following:



simulate this circuit
That will consume less than 14mA all the time, but I'm not sure what value of R1 you would use.  The value depends on the current/voltage curve of the diode and how much current it takes for the Zener to hit 3.3V
Neither circuit will regulate all that precisely, and neither will do well when the load (nRF24L01) draws current in burts - which the nRF24L01 will do.
You can add a couple of capacitors in parallel to the nRF24L01 to handle the bursts, but that won't do anything for the poor regulation or for the fact that both of those regulators are wasteful.  Both waste power all the time - even when the nRF24L01 isn't doing anything.
For efficiency, you need a buck converter with a low quiescent current.
Something like the LTC3388 would do the job.  It consumes less than 1 microampere of current, and only operates when the output capacitor voltage drops - the buck converter will be automatically turned off most of the time when the nRF24L01 is inactive.
That's kind of an expensive chip (and you'd have to build a PCB for it,) though maybe you need that extremely low quiescent current for your task.
Alternatively, many not so specialized buck converters are (compared to your Zener circuit) low power and efficient.  Adafruit makes an LM3671 based 3.3V output buck regulator module with a quiescent current of 16 microamperes.  That's still worlds better than your Zener regulator or the LD33V you were originally using.