First check the planting depth - that's the most common mistake. If you buried the peony's root collar too deep, the plant will spend a long time building strength and won't flower. The renewal point (that thickening where the buds grow from) should be at soil level or at most 3-5 centimeters below. If you planted it deeper, it makes sense to carefully dig it up and replant it higher - yes, in spring or fall, but it's worth it.
Another important thing is lighting. Peonies love sunlight, and if the bush is in partial shade or under tree cover, it'll look beautiful but be temperamental about flowering. Buds need at least 5-6 hours of direct sun a day. Moving an adult bush is difficult, but if it's possible - think about rearranging things.
And finally, make sure you're not overdoing it with nitrogen fertilizer. Too much nitrogen gives you lush foliage, but the plant won't want to flower. With peonies, it's generally better to underfeed than overfeed. If the bush is healthy and the leaves are juicy and green, this could be exactly it - nitrogen excess with a shortage of phosphorus and potassium.