If the Klima is working correctly, it needs a ground signal from the CCU to allow closing of the clutch relay coil.

So, pull the Klima and set the CCU on one of the buttons that will normally close the relay (the three buttons on the left).

If you get a ground signal at socket #10, then the CCU is good. However, I'm guessing that the CCU isn't providing the ground signal to the Klima. It's a typical failure mode of the CCU.