The circuit is a mess:
1) The 2-wire electret mic's ground terminal isn't grounded and its output terminal doesn't have a 10k resistor to a 4V to 9V source for its approx. 0.5mA of current and to allow a few volts DC across it.
2) A comparator has a voltage gain of a few hundred thousand therefore can't be used as a mic preamp. It won't work anyway with its inputs a few volts apart and without a load resistor.
An opamp should be used as a mic preamp. It should have its input properly biased and have negative feedback (comparators can't have negative feedback). Its input should be coupled from the mic with a coupling cap. Its output should be coupled to the trigger pin of the 555 with a coupling cap.
The trigger pin of the 555 should be held high with a pullup resistor.
Then the mic will work, couple its signal to the opamp mic preamp and its output will couple to the trigger input of the 555 for it to produce a timed pulse to clock the counter.
3) The counter's output will be random at power-up since it won't be reset.
4) The counter 's 7th divider's output will go high on the 128th hand clap.
The circuit doesn't have its ouputs gated to produce an output after only a few hand claps. Outputs of a ripple counter can't easily be gated anyway.
5) The circuit doesn't have a way to turn off the relay, nor a reset for the circuit to work the next time.
6) D4, D5, D6 and R2 (the second R2) aren't needed. When the output of the counter (or a gate) is low then the transistor is turned off through a series resistor. When the output goes high then the transistor is turned on through the series resistor.