If you replace the resistor/transistor with an n-ch power mosfet, and replace the relay/prot diode with a light bulb, you'll have a simpler circuit that replicates the circuit you posted (assuming it drives a light bulb with one end connected to +12). If the Fet is chosen carefully, it won't need a heatsink, and the whole circuit can be made on a connecting block and have insulating tape wrapped around it.
THough having just said, the circuit you posted switches on when there is a voltage applied. You didn't describe the existing LED circuit you wish to interface to. Can you tell us more about the LED circuit? How is the LED driven?