I'm not familar with your particular radar detector. However, I had a similar application several years ago. Most radar detectors have some sort of a light that illuminates at the same time as the sound emmits. If that is the case then you can take advantage of that power source.
What you have is a piezo electric buzzer, although it is really classified as a speaker, the arrangement you currently have is equipped with a driver rated at 12 volts. So, when you apply 12 volt power (in the proper polarity) it will emit a very loud tone.
Now go back to your radar detector and open it up. Find the two leads that go to the light. Using a volt-ohms meter, measure the voltage on the back of the light and note the polarity. If you have anywhere between 9 and 13 volts, then this is the place where you can tap into to make your external buzzer scream when the light is illuminated.
Of course, if this is a newer technology radar detector, then it is probably equipped with LED's rather than a 12 volt bulb. If that is the case, then you'll only see about 3 volts max on the back of the LED. At that point, you are going to have to add a transistor in order for the 3 volts to switch the 12 volt buzzer. Yes, you could do this with a relay, but you are making this a much more complicated project at that point.
The project that I did this with was over 20 years ago and I had remotely mounted radar detectors on both the front and rear of my vehicle. I went directly to the 12 volt bulb to drive a piezo buzzer. It worked great. Radar detectors have came a long way since then, but the basic idea remains the same.
Hope this helps.
-K