I would go with the Asters as the Rus. Sage will soon smother them. Will not hurt the Peony plants at all to mix the asters in.

If the peonies are established clumps of a good size, in my experience they will withstand any attempt at encroachment by other plants. So you can plant other, later blooming things next to them. The peonies have nice dark green foliage to act as a foil for the blooming plants. My peony clumps have a number of companions rubbing shoulders with them, particularly asters, purple coneflowers, daisies, hardy hibiscuses and 'Pink Beauty' potentilla shrubs.

I think it could work if you have at least a foot or two of space in-between the peonies. You could also plant late rising plants like Eupatorium 'Chocolate' and balloon flowers in front of the peony. Those perennials would stay short while the peony is in bloom in spring and by summer grow up to partially hide it.
CMK

I treat peony foliage as architectural - it's very nice in and of itself, stands on its own merit and makes a lovely deep green backdrop for other plants. So I agree with planting things around them so blooms/foliage can play off each other, but wouldn't want to smother/hide them with other plants.

If you mean literally 'cover the old foliage' then I would advise against . No plant actually likes to be 'covered' by something, unless it is dormant at the time of covering. They have to build carbohydrates for the next year growth. They can't do it without light.

I know this is a perennial forum but... This year I sprinkled Zinnia seeds behind the peonies it looks good they are growing up into the bush and it looks like the bush is blooming again.

I planted Giant Zinnas from Burpee.

Russian Sage would work. It's a plant that would let light through. It's not a very thick plant and can be pruned as needed. If you're worried about the Russian Sage getting too tall, try the cultivar "Lacey Blue." I plant Russian Sage with Baptisias and Roses. Neither of those has suffered any. I'm sure a Peony can tolerate its presence.

mx gave teh answer ....

plant taller things behind .. shorter things in front.. and give them enough room.. that you are not digging in the peony roots ...

if you damage the large sweet potato roots structure of the peony.. it will take a long time to recover .. if at all ... i would not dig within 12 to 18 inches of the peony ...

mine.. by late summer.. they are covered with morning glory that is supposed to grow up the fence 2 feet behind.. by then.. energy storage is completed ...

ken