The motor on my heat pump went out. I have read that if your heat pump has been shut down for more than a hour you cannot turn it on right away. We replaced the motor is it okay to just turn it back on?

To over-simplify things, if a refrigeration system (a heat pump is a refrigeration system) is shut down, it should not be restarted in less than 5 minutes. If your heat pump has a crankcase heater and that has been shut off for half a day or so I would recommend whatever the manual says. If no crankcase heater, then start it up.