Q.Pruning an older plum tree
The tree only has leaves on 1/3 of the branches. Can I, or how, can I help this tree?

Mature Plum Trees should be pruned in mid summer.
In good growing conditions a Plum Tree can live 20 to 30 years.
You may want to consider a soil test to determine if the soil is lacking nutrients.
Here are some links to help refresh you on the care requirements.
https://www.gardeningknowhow.com/edible/fruits/plum/plum-tree-pruning.htm
https://www.gardeningknowhow.com/edible/fruits/plum/growing-plum-trees.htm
https://www.gardeningknowhow.com/edible/fruits/plum/plum-tree-diseases.htm