Hornbeam backbuds easily.
In Autumn, I would cut the branch on the right, leaving a 1 cm stub. New buds will develop at the base. Select one that will become the new branch, and let it grow. If you proceed the same way with the top (selecting a new leader), you will have a very vigorous grow.
If you haven't repotted it in the spring, you can then defoliate the new branches in June, then trim them and wire them. They will ramify and you can re-structure it.
Hornbeams are very resilient and it will work if the tree is in a good soil and well cultivated.
The base of the tree is very interesting and it shoukld become a bonsai with character. IMHO.