You may see a little more growth over the next few weeks. I've never seen much growth after bloom. Next spring though, watch out! Your plant should be much bushier & taller. Be sure & post pictures when it blooms. What kind of peony is it?

Most plants are like people. They start out smaller, become a teen ranger, as adults the plants may bloom or may wait for more maturity before blooming.

Watch for the stalks to grow taller and the leaves to become larger and less tender before summer. Then depending on the year and peony the leaves may turn autumn colors before being frozen this fall. Even if it does not bloom this year watch your plant to familiarize yourself on it's various stages. Although most plant for the flower some peonies have a place in the landscape after bloom.

The stem should continue growing, but the bud may abort and not become a flower this year, if it does don't think something is wrong. Peonies make an attractive full green plant all summer after blooming. There are a great many species of peony and the growth habits vary a lot. I enjoy all the variations. Al

Thanks for the responses.
I later found some info here-
http://www.paeonia.com/html/peonies/about.htm#7

I got a collection of 5 from Terra Ceia - Edulus, Felix Supreme, Festiva Maxima, Sarah Bernhardt, Jules Elie. Put them in last fall and I see 2-3 flower buds on all of them
I also got Karl Rosenfield and Sorbet from Walmart this spring - those are also growing, but I dont see any flower buds on them. Last year I had plated a red flower peony from Walmart and I was very late in putting in into the ground. I shot up 2-3 shoots and then just died. Now it has 3 nice big shoots with atleast 1 flower bud. So now I have 8 peonies! I will remember to post pictures.

Here is a link that might be useful: FAQ on peonies