NO Relay Triggered By a Proximity Switch. I'm ignorant, don't know what to look for
The big question is what exactly it means for the chuck key to be in the holder, and how that is sensed.  Once you have a electrical signal of some sort, it should be a simple circuit to use it to drive a relay.

A nomally-open (NO) relay sounds like the right thing here.  The relay has to be energized as a result of the sensor indicating the chuck key is in the holder for the unit to turn on.

The circuit could be as simple as a low side NPN transistor, emitter to ground, series base resistor, and relay between collector and the power supply.  24 V is a common relay voltage, so finding a relay won't be a problem.  Make sure to add a diode across the relay coil in reverse polarity to give the inductive current a place to go when the transistor shuts off.

The above works when the detector signal is high when you want the device enabled.  If the other way around, then a high side PNP switch works.  It's basically a mirror image of the low side NPN switch circuit.

We can get into details once you have some real specs on the detector.