Arizona Ash Help

Purchased this home last year and know next to nothing about trees.

This Ash (SW Texas) struggled after an ice storm that came through a few years back. That and drought seem to have caused some damage at the top of the canopy. I watered it quite a bit since purchasing the home and there’s been quite a bit of growth in the middle of the tree but the rest of it has stayed dead and/or brown.

I’m looking for advice. Some local trimmers came by and said they need to trim the new growth out for the longer limbs to grow but it seems to me that the dead branches/limbs need to go…