The traditional way to make aspic is with meat juice mixed with gelatin.
Bloom a packet of unflavored gelatin in 1/4 cup of water then add meat broth. If you want to have bits of meat or cooked vegetables, let the gelatin set, partially, in the fridge before adding the extras. Otherwise, just put it in the fridge until it sets.
It's kind of hard to make jelled meat without using gelatin. You'd have to boil a chicken carcass to make bone broth. Boil for a good, long time to make all the collagen come out of the bones then put in the fridge until it gells.
Gelatin is made from collagen taken from animal bones by boiling. Whether you use powdered gelatin or boil your own bones, you're ending up with the same thing. It's a lot faster and easier to use gelatin. You get more consistent results, too.