Help with my OLD Live Oak

[ATXdesign]

I am lucky to have some really beautiful and old Live Oaks on my property. They are all healthy and beautiful except for this one that has/had some damage a while back before I bought the land. One of my trees looks like half of it is is dead but the other half of the tree looks healthy and strong to me. I'm wondering if any professionals have any thoughts or advice on what I should do for this tree. Should I start cutting the old dead limbs off? Will that offset the weight of the tree and damage it? The healthy side of the tree has limbs growing down to the ground although now sure if these would provide much support at this point. Should I leave the dead side alone on the main trunk or should I do something for the tree? Does it look like the tree will survive? I know these trees are super old but not sure how old this damage is. Sorry for all the questions but thank you for any help.