Planning permission is not normally required for fitting insulation.
External wall insulation
External wall insulation (EWI) comprises a layer of insulation material that is normally attached to external walls with mechanical fixings and adhesive, and then covered with protective layers of render or cladding. The finish covers the whole exterior of the building, including existing brickwork.
EWI must not project more than 16cm from the external wall of your property. EWI which projects greater than 16cm will require planning permission. If you live in a Conservation Area, a National Park, an Area of Outstanding Natural Beauty or World Heritage Sites, you will also need to apply for planning permission.
Welsh Government has produced a leaflet which can help you think about the issues around installing external solid wall insulation on your home.
The Welsh Government has produced a technical guide, and a householder guide, available here, to help you understand how permitted development rules might apply to your circumstances.