Certified GKH Gardening Expert
If the sucker growth has roots on it, then yes, you can replant it elsewhere. If you dig around the base of the sucker, check to see if it has its own root system. If it does, you can simply dig it out and cut it away from the parent plant. Then place it in a pot and give it plenty of water until you see new growth. Then it can be planted out in the ground.
If you do not see that it has its own root system, scrape a little bark away from below the soil line on the sucker and then cover the wound back up with soil. Check back every month or so until you see roots develop and then follow the instructions above.
You will want to help shape it as it grows, because most suckers want to grow more like a shrub than a tree. However, a little pruning will fix this.