I have a huge maple tree in my yard. The diameter of the trunk is over 15 feet. Would it make sense to plant 1 climbing hydrangea on opposite side of the tree to speed up full coverage of the tree?

Thoughts?

Yes. While CH is not aggressive, it may compete for nutrients so just ensure you fertilize the area. If growing it on a short-lived maple tree like a silver maple, ensure the tree will still live for a while as CH can live well over 50 years (which is much less than other types of maples' 400+ age estimates though). Enjoy. Like wisteria, expect it to start blooming a long time from now.

Do you mean circumference? I'm trying to picture a maple with a 15-foot diameter trunk.

In my comments, I assumed 'circumference' as my maples do not normally get that big. But some Comfort Maples can hit a circumference of 20 feet.