Cheltenham Borough Council names seven conservation areas: the Central Conservation Area, Cudnall Street and Bafford in Charlton Kings, Poets in St Mark's, Prestbury, Swindon Village and St Mary's. It says the central area "covers around 599 hectares" and has been "split into 19 character areas", and that applications in a conservation area "must demonstrate how the proposals would preserve or enhance the character of the area". On Article 4 it states "In Cheltenham there is currently only one Article 4 direction", which "withdraws permitted development rights to change the use of a building from a Class C3 use (dwelling house) to a Class C4 use (house in multiple occupation)" and "only applies in the geographical area edged in red on the direction itself", in St Paul's. That direction concerns change of use, and the council names no Article 4 direction covering boundary treatments in the borough.
The Planning Portal sets the national rule behind every Cheltenham job. It says you will not need to apply for planning permission to erect a new, or alter, maintain, improve or take down an existing fence, wall or gate where it is "next to a highway used by vehicles (or the footpath of such a highway) and it would not exceed one metre in height (from ground level)", or where "it would not exceed two metres in height (from ground level) if elsewhere". Where a Cheltenham boundary already exceeds those limits, the condition is that "its height would not be increased".
Those conditions also require, at a Cheltenham address, that "no part of the site is a listed building or within the curtilage of a listed building", that no part of the boundary "forms a boundary with a neighbouring listed building or its curtilage", and that "the right to put up or alter fences, walls and gates has not been removed by an article four direction or a planning condition". In a Cheltenham conservation area it says "you might need permission take down a fence, wall or gate".
In Cheltenham we would explain how you check the conservation boundary, any Article 4 direction and the proposed work before confirming whether permission is needed.