As you now want to have a variable timed period I've modified the circuit so that it can be set anywhere in the range ~1.5 - 7.5 hrs just by adjusting variable resistor R4.
Note that in the new circuit (attached) :-
a) R4 is now 250k, R3 is 68k.
b) Pins 5 and 6 of the CD4093 are now separated and are connected respectively to pins 2 and 1 of the CD4060 so that the beeper pulses coming from the alarm clock are blocked for 3/4 of the timed period, i.e. for at least the 1 hr that they persist. That enables periods down to ~1.5 hrs to be timed.
c) The relay is now driven from the Q14 output (pin 3) of the CD4060.
As an indication that the timer is working, the R2 LED, driven by pin 9 of the CD4060, flashes at a rate ~ 137/T, where the rate is flashes per minute and T is the period in hours. [The R1 LED flashes at 1/16 that rate].