I don't think you can put your old trailer plates on the trailer, but I would check with the licensing authourity in Alberta to advise you what you need to do to tow it from the border to your place. You should be able to get some type of permit.
When I purchased my boat and trailer in the US, the trailer had current license plates on it and the previous owner agreed to leave the plates on the trailer until I got back to BC. (I then sent them back to him.) I had to pull the boat through 3 US states and they all have different requirements if there are no plates on the trailer, so this made it a lot simpler. I also purchased what is called "Binder Insurance"(in BC) which gave me insurance coverage while I was towing the boat back to Canada and allowed me to tow it from the border to my house. Once I had it at my house, I got a one day operating permit to have the trailer inspected by Canadian Tire and then had it licensed by ICBC.