Fairly simple to do, connect a relay with a back emf diode across the collector load (R13 and D1) of Q1 in the right hand circuit you have posted.
Use one normally open contact of your relay to then switch the PSU to your second circuit as the diagram shows.
The relay coil voltage should be chosen to match your supply voltage.
Should you want your combined circuits to have the Sounder section remain 'activated' after triggering, use a second contact which makes to connect between the collector and emitter of Q1, with a Reset push to break switch in series.
hope this explains it OK
Mik