peony tree strange growth from bottom

I have been living in this lovely rental house and my favorite plant of all is a peony tree in my front yard. It usually produces 4 - 5 flowers each year but this year it only had three buds and one is from the base. Two of the buds have opened (including one at base) and there is a third, much smaller preparing to open. The flower growing from the base is lovely and big, however it's leaves are different from the other ones on the rest of the plant.
I have lived here for 10 years and it appeared to be an old plant when I moved in.
Can you advise me of whether or not I have a problem on my hands? If so what should I do?
I have included pictures of the tree.

 

If the flower is the same and only the foliage is different on the stalk from the base , maybe just leave it for now and see what happens.
If both the flower and the foliage were different , it would likely indicate sprouting from an herbaceous root stalk. Tree peonies are often grafted on to a herbaceous nurse root which can send up a herbaceous stalk years later and should be removed.
For some, the flower form can change as a plant matures, like a single can change to a semi-double or double flowered form over the years. Some can have single, semi-double, and/or double flowered forms on the same tree peony. I don't know if foliage changes much though.
They don't seem to like much root competition.

 

Thanks Chimera,
The flower is the same, so I will take your advice and leave it for now. I have also read mixed opinions on whether or not you prune off the dead branches. I feel that sometimes it looks as if a part of the tree is dead wood but then a new piece grows off of the dead looking branch the following year. Do you prune your peony tree?

 

Yes, have been pruning cautiously. The deadwood is easily removed in February, cutting the branch back to about an inch (2.5 cm.) above a live bud. The remaining stub can be removed next year. I haven't thinned out any live stalks yet.
A couple videos, by KelwaysPlants and Cricket Hill Garden, may help.