6′ holly tree
One side was originally against a 4' bush and that side has not shown any growth. Is there a way to start growth there? It is a front garden with full sun.
Unfortunately that side of your holly may have died off. Lack of sunlight and air circulation may have been the cause.
You can test the branches. Do they bend or snap off? If they bend you may just wait and see if the plant may leaf.
If you have not fertilized yet this year, you could add a balanced fertilizer.