Certified GKH Gardening Expert
If this is a plum tree that you get fruit from, I would certainly take the sucker down as it is drawing energy from the parent tree, which will affect its fruit production. If it is a decorative plum, you can remove it if you would like, but it is up to you. The sucker will still be sapping energy from the parent tree, which can slow its growth, but it should not cause harm beyond that. If you remove the sucker, be sure to use sharp, clean pruners so as to reduce the chances of disease getting in the wound.