Where does the power come from that activates compressor clutch

A/C compressor clutch engagement is dependent upon the A/C compressor signal. Because a new compressor was installed, we can assume the clutch and field coil (electromagnet) are fully operational and should focus on the A/C signal instead. The field coil receives signal/power from the A/C clutch relay which is powered by the A/C clutch fuse (10A); both are located in the under-hood fuse block. The A/C clutch relay is controlled by the powertrain control module (PCM). The PCM monitors inputs from the A/C refrigerant pressure sensor the body control module (BCM) to know when to activate/deactivate the A/C clutch relay. If the pressure (refrigerant charge) is too low, it will not activate. Likewise, if the BCM doesn't send an A/C request to the PCM, it will not activate. The BCM monitors inputs from the HVAC control module and evaporator temperature sensor. If the A/C request switch is not turned on in the HVAC control module, the A/C request will not be sent to the PCM. Likewise, if the evaporator temperature sensor indicates the evaporator is too cold (whether true or not), the A/C request will not be sent to the PCM. You can read more here: https://www.yourmechanic.com/article/how-long-does-an-ac-compressor-last

You need to start at the beginning. What activates your A/C? The dash controls.
Stat cool !

Is the AC clutch any good? Is it receiving power to activate the compressor?

Laurie, why bypass the compressor? - even if it is frozen, as long as the AC clutch is not activated there will not be an issue. To be safe just disconnect the wire powering the AC clutch.

unless you have a problem in the pulley bearing of the ac compressor , just disconnect the power wire to the compressor and use the standard belt
the pulley is just an idler pulley until the clutch is activated so if there is no power to activate it it is just an idler

Has the Freon been checked with a gauge to see if there is enough Freon to allow the system to work. Low or no Freon will not allow the compressor to engage. The low pressure switch is most likely activated due to low freon, and will cause this condition.

{: ) The a/c blower controls is independent of the a/c compressor system. Meaning, the blower can still deliver air even if your compressor system is not working or not cooling.
I assume your blower functions are okay, since you are now focused on probing power to all those connectors near the compressor.
If I imagine it right, the first plug you pulled has three wires on it and it should be the a/c refrigerant pressure sensor. The next plug you said where the a/c clutch is, has two wires on it, and obviously that's the a/c clutch/compressor connector. Just for safety reminders, never apply direct 12v power to any of those plugs that you pulled, especially the pressure sensor, because you may damage the PCM and other components and will only worsen the problem. I'll show you a sample diagram of the compressor controls just to give you an idea. A/C Controls 101:

The red lines indicate the flow of 12v power once the relay is energized. Power from the battery flows thru the A/C CLU fuse at the underhood fuseblock (you can check this fuse if busted) and then flows thru the a/c relay (you may also substitute a similar relay for testing) going to the compressor. This continuos flow happens only when the relay is activated.
The green line indicates the request signal coming from the PCM to energize the relay. The PCM monitors several inputs like the pressure sensor inputs, the a/c control switch on the dashboard, the engine temp, and others. Based on gathered inputs it will decide when to give a request signal to energize the relay that will activate the compressor.
So you see, if one of the inputs do not agree, or if there is a fault on the engine sensors, the a/c controller, or the PCM itself, no 12v power will be present on the a/c clutch connector.
The fuse, relay, and clutch can be easily tested with basic tools like the test light or multimeter. But if the fault comes from the control signals, you will need a more comprehensive diagnostic approach. A scan tool is very effective in diagnosing signal faults.
You may need to check also the refrigerant charge. So goodluck.

Compressor uses a clutch that is activated electrically by a relay. When you turn on the A/C, you should hear the clutch engage and pull power from the engine. If the clutch is not engaging, there may be several reasons:
wiring problem
HVAC switch failure
relay failure
compressor clutch failure
low refrigerant level

There is a sensor that checks the system return pressure and will not allow the clutch to engage if the refrigerant level is too low.

Look in the under hood fuse box it is usually among the sensors within the box.

I think what your mechanic is saying is that the clutch mechanism on your A/C compressor is bad. What this is "a magnetically controlled clutch which activates the A/C compressor and allows it to work"
so without the clutch the compressor will not function as it should.