I made circuit as shown in picture. Output signal is connected trough resistor to base of transistors. The waveform at the output is correct but signal amplitude is 9V. I expected amplitude equal 24V. Could you please help me a litle bit. Why it dose not work
You need a driver with level translation, more than two transistors are required to make it. Why don't you use an off-the-shelf integrated driver like TC427?
If you need more source current then decrease R2.
If the output_voltage_low of the NE555 is too high, then add a 10k at B and E of T1 (to safely switch T1 OFF).