Automatic 12V plant watering system?
(EDITED) - Notice that the last Nand gate ahead of the beeper looks to be a slow oscillator, (the beeper likely rings as ON-OFF-ON-OFF....). The input to the last Nand changes from being either a low signal or a fast square wave signal, (which corresponds to wet soil then to dry soil conditions). 

The diode in the feedback of the last Nand actually makes things a bit more complicated as it has an uneven charge/discharge affect on C3.  The result is that the last Nand outputs a gated burst of the square wave pulses at a low duty cycle when the soil is dry (giving a Beep-Beep-Beeping).  Then when the soil is wet the output is just a high, which keeps Q1 turned off (and noda Beeping).

Since the active signal is a bunch of fast pulses it would be best to converted this into a simple DC voltage or a single pulse that can easily drive a DC motor, (or a relay coil).  One solution would be to create a small AC-DC converter then use this as the input for a motor driver.

The circuit below can take a continuous stream of pulses or a quick burst of pulses and convert it into a DC voltage or a single DC pulse for driving a DC motor.

The NPN and diodes are not critical, (2N3904 transistor and 1N4001 diodes would suffice). Q1 takes the 3v pulses and converts them to 12v pulses, they are then passed as AC and rectified by C1-D1-D2. The rectified DC builds up on C2 and turns on Q3 which controls the motor.  R3 discharges C2 after the AC input stops.  Increasing the value of R3 could extend the width of a DC pulse if needed, (for example if input was taken from the beeper top end).  D3 shorts out any spikes from the motor switching and C4 helps reduces motor noise on the +12v line.  The NMOS part would need to be selected to safely pass the maximum current of the DC motor.

The "INPUT" for this circuit could be from any of the points with the AC (water me) signal, for example: Nand gate pins 3-5, or Nand pins 1-2-10, or even the beeper high end (above the resistor) if short DC pulses into the motor are acceptable.  In this later case the motor would run only for the short time the beeper normally sounded.

As before, you may want to keep the beeper in the circuit for testing and for a warning in case the watering jams on for any reason.  A nice effect of using an AC-DC converter circuit like this is that if the input were to jam high or a low the output will not turn on the motor.