The area that is turning white could be caused by a broken branch. Maybe due to handling while moving and planting or due to ice and snow. It could also be that it was too dry over the winter. You might take a small cutting along with a picture of the whole plant to your local garden center. They could help diagnose the problem and find a solution.
MY ARBORVITAE EMERALD GREEN IS TURNING WHITE – ANY HELP?
That doesn’t sound good! Is this a new plant or one that has been in the ground for a while?