North Somerset Council says that in a conservation area planning permission is needed for, among other things, "demolition of walls, gates and fences which are one metre or above and next to a highway, including a public footpath or bridleway, waterway or open space" or "two metres or above elsewhere". On trees the same page says "you need to give us six weeks' notice if you want to cut down, top or lop a tree in a conservation area".
The Planning Portal lists outbuildings as permitted development subject to limits, among them no outbuilding on land forward of a wall forming the principal elevation, a maximum height of 2.5 metres for a building, enclosure or container within two metres of a boundary of the curtilage, and no more than half the area of land around the original house covered by additions or other buildings. The same page says that on designated land buildings at the side of a property require planning permission, that within the curtilage of a listed building any outbuilding requires planning permission, and that the allowances do not apply to flats and maisonettes.
The council's Article 4 Directions page carries five Clevedon documents, three for a Clevedon conservation area and two for the Clevedon Triangle, and the council says an Article 4 Direction can void permitted development rights for works that usually need no permission.
We would explain how you check the conservation boundary, any tree preservation order, any Article 4 direction and the proposed work before confirming whether permission or notice is needed.