I get the same beeping on my Carbon Cub since the ESC was replaced by the one from my C-pack. The Carbon Cub's receiver does some complicated initialisation because of the GPS in it. The ESC beeps continuously from the time I plug in the battery until the Receiver gives the signal that it's ready to go. During that time, I can't operate any control surfaces or the motor. This means that the beeping must be because it doesn't get a "ready to go" signal from the receiver, so my reckoning is that you have to look at the receiver tom solve your issue.
If you still think it's the ESC, you can prove that by disconnecting it from the receiver and using a 5v battery/supply or USB supply to the receiver to power it. The servo should then work unless the problem is in the receiver.