What will be the effect of adding a 10k load resistor to this circuit?
The circuit attempts to deliver 5 mA of current into whatever is connected between the collector and ground (presumed to be the lower node in the circuit). This current will vary a bit with a changing power rail (Vsupply) but I have assumed 5 mA.

ZD2 (a 5.6 volt zener) ensures that there will be about 5 volts across the emitter resistor R1 (1 kohm). This means that with a fairly decent accuracy, the current into ZD1 (the collector current) will be about 5 mA. Given that ZD1 is a 5.6 volt zener and that a 10 k resistor is then placed across it, the current into the 10 k resistor will be 0.56 mA. So, now the ZD1 current will be 5 mA - 0.56 mA = 4.44 mA.