I'm not sure what the proper answer should be, but I would plant it out. I grow lots of plants in pots, including Peonies, then plant them when I've found the right spot for them.
Just make sure they are well watered. If it's overwintered in the pot and got a bud it should have a decent enough root system in my view.

I've no idea whether you even live in the UK so... what is your weather like? By now I would have expected your peony to be in flower, ours all are. If you have a site ready for it and can keep it well watered over the summer then you can consider planting it in the ground now but it will be easier to do in the autumn when the leaves are dying back.

My Sarah Bernhardt is still at the bud stage, in NW England. Whenever you plant it, make sure you don't bury it any deeper than it is already. Good luck!

Agree Melchisedec if it important not to plant in the ground deeper than it is in the pot.

I have a Sarah Bernhardts that were just a dried roots. Planted very near the surface( 2 of them) a few weeks ago, and one made a bud almost right away. I was surprised, but I doubt it will come to a flower this year. I must nip a bit off the old Bowl of Beauty and have a go with that. Good luck with your peony.....it doesn't look like they are all that fussy. Just plant really shallow as advised.

thanks for the answers to my peony problem.i live in the shetland isles so we are at least a month behind the rest of the country.think ill wait till she flowers then plant in ground

Very wise Helen, you must have quite a challenge gardening up there.