I have a mini patio President plum tree inherited when moved in. It has been planted in the ground and is rather large. I think it's about four years old, but so far has not even had any blossom on it.
Plum Tree No Blossoms
Certified GKH Gardening Expert
Your tree may not be quite old enough to bear fruit just yet - it can take up to 6 years. Does your tree get enough sun? Are there any signs of disease or insect infestations?
Here is an article that explains why plum trees do not fruit: