Designing a Light/Dark Sensor with LDR 555 alternator LED and Motor
In your circuit you are hoping for the current to run through the motor, through Q1, R6 and D3. The problem is that R6 is 470 Ω so the maximum possible current you could get through that leg of the circuit on a 9 V supply would be \$ I = \frac V R = \frac 9 {470} \approx 20\ \text {mA} \$. It's even worse than that when you take into account the voltage drop caused by Q1 and D3. Even 20 mA probably won't be enough to start the motor.

Figure 1. Next steps.
Try rewiring as shown here.

Run the LEDs directly off the 555 output.
Connect Q1's emitter to ground. Now you've made an &quot;open-collector&quot; arrangement that can sink the motor current to ground. You will have almost the full battery voltage across the motor and it should easily run up to speed.