The clutch is there. The rubber has separated from the clutch plate. That 10mm nut is connected directly to the compressor shaft.
The rubber is a dampener like an engine harmonic balancer. Your rubber has separated from the metal its supposed to be bonded too
When the clutch is powered up it turns into an electro magnet pulling the clutch plate forward into the drive pulley which is the one with the belt on it And thus turns the compressor pumping the aircon gas around the system.
Thats whole front plate is just a friction disk made of metal just like a car clutch.