Q: My ac clutch is not engaging, but there is no relay in the fuse box for the ac compressor

If a mechanic told you only that the compressor is not "engaging" that is essentially a useless diagnostic because it is too cryptic and too vague. The compressor in the system will only operate if the compressor clutch is engaged. That clutch is electrically controlled. So, if the circuit controlling the clutch includes a relay but the relay is missing, you should replace the relay. Be sure to use the right relay with the correct electrical rating. If you are unsure if a relay is in the the circuit, you can determine what is supposed to be in the circuit by consulting the Factory Service Manual wiring diagram.

With regard to this vague diagnostic, "compressor not engaging", if the fault is the clutch simple causes for clutch failure have to be evaluated, so, in addition to a missing relay, you could have a broken wire to the clutch or maybe the clutch is bad. The clutch can often be replaced without replacing the compressor and indeed without even discharging the system (a huge plus). To get your a/c fixed at the LEAST possible cost, what you need is an intelligent, authoritative and conclusive diagnostic stating EXACTLY what is wrong and why. If you request an a/c system diagnostic YourMechanic will dispatch a certified mechanic to your location and get the system properly diagnosed and once diagnosed the mechanic will explain any required repairs. If you have further questions or concerns as you decide what to do, do not hesitate to re-contact YourMechanic because we want you to make the most of your repair dollars and help you get the best possible results.