Question

new growth  

splits   I moved into a home 7 years ago and this tree was here.  I think it is an American Chestnut.  I would find a few of the prickly pods in the spring.
In the past it looked to be doing well but this spring it did not leaf.  The trunk has many long splits in it.
Just in the past month new shoots have sprouted from various places on the tree.
Is there anything that can be done to save the tree?

Answer
Sounds like Chestnut blight. the tree looks like it is dead. You could cut the dead parts off and see if it can recover but with chestnut blight there is little hope. Sorry! Here is a web link to info about this disease. https://treecanada.ca/en/resources/tree-killers/disease/chestnut-blight/