Hello Aimee, and thank you for contacting us at the UVM Extension Master Gardener program with your question.

What a beautiful old apple tree in your yard - I can see why you'd like to keep it growing!

While apple trees have a finite lifetime (somewhere between 50 and 100 years for non-dwarf varieties), as you can see with yours, there are younger portions that are thriving.  It is recommended that you trim away some of the dead sections, and then consider gradually pruning the areas with healthy leaves and fruit over the next few years. 

Here are a few articles that review the key approaches for this, with information on the best time and techniques to prune to minimize stress and optimize harvests, as well as some thoughts on shaping the tree to keep it healthy and productive.

https://extension.unh.edu/sites/default/files/migrated_unmanaged_files/Resource000582_Rep604.pdf

https://extension.psu.edu/home-gardening-pruning-to-renovate-old-fruit-trees

https://catalog.extension.oregonstate.edu/ec1005

I wish you luck with keeping this impressive tree as part of the landscape near your home for another 25 years!