Simple LED fade circuit
Firstly the warning: -


  the problem is that I can't reach the full brightness of the led that
  it reaches when simply connected to 12v power supply


Don't connect a standard LED directly to a voltage supply unless you want to risk breaking it - always use a current limiting resistor.

Back to your schematic; you are using an emitter follower to drive several series LEDs and this naturally loses about 0.7 volts between input (base) and output (emitter) and this might explain some loss of brightness. To restore the current, try lowering the resistor in series with the LED string but heed the warning about it being a current limiting resistor and don't make it so low that you damage the LEDs.

You are also using a potential divider to drive the base and this naturally reduces the base voltage and, in turn, this naturally reduces the emitter voltage. I would move R2 to the left of R1 and make it lower in value than R1. For instance, if R1 is 10 kohm then the newly positioned R2 should be about 1 kohm.