In theory, you can graft a branch from the tree to the site of your choosing. However, you can't graft a big branch and you have to deal with why the dead branch died. Usually, a tree will produce a new branch where there's an opening, such as in the space left by a removed branch. I'd certainly wait a year or two to see if this happens. Grafting is pretty tough to get to work.

the tree is taking on a new form... accept it.. its old form is gone..

unless you have decades of grafting experience.. i doubt you can graft a tiny piece on an old mature tree.. though weirder things have happened..

give us a few pix.. and let us help you prune it .. rejuvenation pruning comes to mind ...

the past is dead and gone.. accept it.. and move on .. with no insult to the root mass.. and presuming the plant is otherwise healthy.. you might be surprised how fast is can regenerate ..

do we have any idea why that part died???

ken