Loose A/C compressor pulley

Unfortunately your pulley has broken and needs to be replaced along with the compressor clutch.

However, if it were me I would just replace the compressor and recharge the system. A lot of times this broke because the compressor is locked up. So the fact that the pulley is broken you are not able to see if the compressor is spinning. If you replace the clutch and pulley and then find out the compressor is locked up then you are going to have to replace it all again with the new compressor.

Here is a guide that will help with this:

https://www.2carpros.com/articles/replace-air-conditioner-compressor

https://www.2carpros.com/articles/re-charge-an-air-conditioner-system

Below is the process from the manual as well.