A/C Electrical ground wire

I am installing a low profile Penguin heat pump on my 1961 Tradewind. The trailer previously had an A/C unit installed, though that was removed some years ago and replaced with a vent. The original 120 two wire wiring is in place. Here is the question - run new circuit for the A/C or use the existing, and if so, what about the ground? I upgraded the basic electrical in the trailer with a converter and have run a couple new dedicated circuits, such as for the electrical element on the lp/electric water heater and microwave.