to ATP.
I don't think I have ever seen a Madagascar palm (Pachypodium lamerei) quite that big! The lower part of the "dead" branch is still green. I suspect, given time, it will grow new buds somewhere along the length of that branch. Give it time.
Please add location info and possibly your hardiness zone to your information. It will help in the future to know where you are and what your growing conditions are. Someplace warm and sunny considering the photo of your palm.
Daisy