Using a NE555 for 12V boost to 24V to power an amplifier
It requires 21V to 24V power supply and about 6/7A of current at 24V.
  The input is a car battery: 10V to 14.4V.


So the output power is about 22.5 volts x 6.5 amps = 146 watts.

Forget the circuit you have shown because it might deliver a couple of watts at best. Go for a proper boost regulator to step up 12 volts to 24 volts. Something like this: -