Here is a picture from another forum of new tree peony growth.
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here is a picture of a true herbaceous sucker
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they look quite different. Yes, you can let it grow a few weeks to see what it looks like, but the herbaceous rootstock can overtake the treepeony rootstock and eventually kill it. And you will be left with a herbaceous peony. Been there and done that. That is a herbaceous sucker. It can come up at the base of the plant (it is a part of the TP root mass), or it can surface a foot away from the base. It doesn't matter. You may not have to replant, just pinch off the sucker and mound more dirt around the TP for now.
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