
The main sign of AC pulley issues is the air conditioner not cooling. Also, you might notice a few other things, like burning smells, odd noises, electrical problems in the car, etc.
A belt called the serpentine belt spins the AC pulley, which is attached to the AC compressor. When the pulley spins, it makes the compressor work; the AC compressor is the air conditioner's heart, so if it fails, the AC won't work. Typically, whenever the pulley or serpentine belt has a problem, it'll cause problems for the AC compressor.
A faulty AC pulley won't transfer power to the compressor, and the air conditioner won't work.

Since the air conditioning pulley is rotating and powering the entire AC system, if it fails, the power stops. If the AC system stops receiving power, it stops cooling.
Inside the vehicle's cabin, the temperature won't lower. The AC unit will be unresponsive, and components won't work due to no power.
Alternatively, depending on damage, the pulley might transfer power, but below what's needed for the AC to work properly. In this case, the cooling efficiency is compromised and won't lower the temperature noticeably.
An issue in the AC pulley can also mean issues in the serpentine belt and compressor clutch, which involve rubber material. For example, the serpentine belt might have slipped out of place, damaging the pulley. In this case, the belt can flap under the hood and rub against hot engine components, melting and causing a burning rubber smell.
Alternatively, the pulley itself can develop an overheating problem, transferring too much heat to the compressor clutch. The clutch can start to melt over extreme temperatures and release a burning rubber smell.
Here are some other signs that a faulty AC pulley can show:
In a pinch, you might be able to drive with a bad AC compressor clutch pulley, especially if it's not seized and spins freely. However, it's risky. A broken pulley can damage the belt, expansion valve, clutch coil, pulley bearing, potentially leading to overheating or even seizing the compressor itself, causing a cascade of expensive repairs. It's best to get it checked by a mechanic as soon as possible.
Bypassing the AC pulley is possible in some cars, typically by installing a special bypass pulley or using a shorter belt. This lets the engine run without engaging the AC compressor. However, it's a temporary solution at best. While it can restore some lost engine power and free you from belt worries, it completely disables your air conditioning and might cause warning lights. Consulting a mechanic for a proper air conditioning system repair is the safer and more long-term solution.
The squeal from a bad compressor pulley likely points to a slipping issue caused by either a worn or loose belt or a failing component within the pulley itself. A worn belt loses grip, while a loose belt needs tightening. The pulley's bearing might be failing due to age or lack of lubrication, causing friction and noise. In some cases, the compressor clutch itself could be malfunctioning.