Debris from Roof causing Gutters to clog
It is generally advisable to not have tree branches making contact with your house, so regardless you might want to consider trimming the branches back.  Removing the tree entirely is probably overkill but is an option.  Make sure to check with your local jurisdiction to see if a permit is required.

Alternatively, you're just going to need to clean them out regularly, especially in the spring and fall.

Even with gutter guards, debris will still find its way into the gutters, albeit it at a slower rate.