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They may either be lacking light or they are lacking in phosphorous. Check the area to see if over the years, they have not become shadowed by surrounding plants and trees. If you feel they are getting enough light, try adding some bone meal to their soil to help get them blooming again.

This article will help:
https://www.gardeningknowhow.com/ornamental/flowers/peony/why-your-peony-buds-but-never-flowers.htm

They will have a hard time surviving because it is a bit too warm, but it is worth trying. I would plant it in a semi-shady location, to make sure it gets some sun but also protection from heat.

I will warn you, peonies are notoriously picky about being moved. When you plant or move a peony, it can take 1-6 years before they bloom.

Remove spent blossoms but do not trim peonies. They need the leaves to produce energy to give you flowers next year and support the roots. I assume it freezes there. After hard frost, you can trim them back, if desired, and clear away ALL debris throwing in the trash, not a compost pile.

Before this question can be answered well, more information is needed. Where do you live? Where is the peony growing (sun, shade,)? HOw long have you had it? How often do you water? What type of soil do you have? Clay, sand, loam? How deeply did you plant the roots?