I've had newly planted peonies sprout in the fall if it was warm for a while here, not that unusual. That growth will die back naturally when it gets cold in your zone and shouldn't make a difference in next spring's growth. I've not had any luck overwintering in pots so I'd plant it in it's new location; depending on your zone you might have better luck than I did, I'm zone 4b.

Thank you so much! I have already replanted it. I just hope it thrives!! I did notice growth on the other peonies and felt relieved, that it must be a normal occurrence. Don't know why I never noticed it before! Again, thank you!

I have some new growth on newly (late summer) planted tree peonies, just noticed it yesterday. Crazy since I stopped watering at least 3 weeks ago and we've had no rain....haven't even had a really cold snap, just a couple of nights below freezing so far.

I guess it's something that they do! I never picked up on that before!