Thank you for asking your question on Just Answer.
Swap the A/C clutch relay with a similar relay and recheck operation. If the clutch now works, replace the faulty relay. If the compressor still does not come on, verify there is battery voltage to terminal #3 of the relay from fuse #25. If OK, jump terminal #3 to #5 in the engine compartment fuse box to bypass the relay (with the relay removed) and check the compressor operation. If the compressor still does not run, leaving the jumper in place, check for battery voltage on the Gray/White (GY/WH) wire at the compressor. If battery voltage is not present, locate and repair the open circuit between the relay and the compressor. If battery voltage is present, check the Black (BK) wire for a good ground. Repair the ground as needed and recheck operation. If the ground is good, battery voltage is present on the GY/WH wire but the clutch is not engaging, suspect a bad clutch coil.
This is a 2003 right?
and this relay panel is in the under hood fuse panel.