I'm a bit of a throw it together person & just of the top of my head, I'd mix the quark with some lemon juice & a little water & make a lemon sauce to go with your chicken.
Or you can add a little stock, seasoning, onions, mushrooms & make a sauce to pour over your chicken.
Or cheese to the quark & make a cheese sauce to add to the chicken.
The thing to remember with quark is it always tastes better after the seasoning has been left for a while.