If your vehicle is showing loud clunking sound when turning on the a/c, here are the most likely causes and the parts you'll need to fix each one.
Over time, the friction material on the A/C clutch plate wears down, increasing the gap between the plate and the pulley. When the electromagnet engages, the plate slams into the pulley with excessive force, creating a loud, harsh clunk.
The sudden mechanical load of the A/C compressor turning on can cause a weak automatic belt tensioner to violently bounce or bottom out against its internal stops, producing a clunking noise.
If the compressor is failing internally or trying to compress liquid refrigerant/excess oil (known as slugging), it will create a heavy mechanical clunk as the engine forces the locked or struggling internals to turn.
When the A/C turns on, the engine computer slightly increases the idle speed and the compressor adds drag. This sudden change in engine torque can cause the engine to shift and clunk against a broken motor mount.
If the A/C compressor was recently replaced or serviced, improperly torqued mounting bolts can cause the entire compressor assembly to shift and clunk against the engine block when the clutch engages.