Installing new panels in concrete fence posts with overhanging tree branches
Cut the panels (horizontally) into strips short enough (vertically) to slip between the limbs and the top of the posts. Stack as many strips as needed to get the full height. 

So if you have 2 feet of clearance and 6 foot tall panels, cut them in to 3 strips, insert each strip. If you have 3 feet of clearance, cut them in half. If you have 18" of clearance, 4 parts...one variant of the type of fence you describe uses strips (boards or sometimes concrete "boards" when going for a "never have to do that again" method) that are only 6" or so tall. Stack 12 of those and you've got your 6 feet (tall.)