I am always tethered to the tree in addition to using my lineman's belt. I am amazed that more people don't do this. It adds maybe 5 minutes to your climb while making it several orders of magnitude more safe.
I have a carabiner on the end of my tether so I can use that to quick connect and disconnect the tether. I use a screw lock 'biner and always lock it. I use a scaffold knot to help keep rope on the correct side.
To keep the 'biner'd tether from sliding down the tree, I have a triple fisherman's knot around the tether that is not connected to anything. This is just a little nub I can slide down the rope to trap the 'biner against the tree and make it tight. The tag end of this slider knot is triple wrapped with gorilla duct tape on the side that hits 'biner to make it stiff and grab 'biner.
When I hit a branch, I disconnect my tether and move it around the branch. I then grab the tree, disconnect my lineman's belt and move it up with the tether.