Yes, and it’s typically recommended. A wallboard insulation can be installed once the old siding is removed. It’s available in a variety of styles, thicknesses and R values. Many come with a housewrap and the joints get taped. Energy efficiency is improved along with air infiltration and noise transmission. By insulating over the exterior wall in this way, it prevents thermal bridging at the wall’s studs, adding to the energy efficiency. In addition, the insulation provides a better surface for the installation of the new siding.