Adding a conservatory as a Barn extension usually goes against planning regulations and is likely to be objected to. Most local authorities planning policies state that “a barn will be granted planning permission only if it is capable of conversion without significant rebuilding or extension.”
If some years after the original conversion has been made you wish to add a conservatory the same proviso applies.
However, while permission to extend is slim you should check with your local council to find out what they may accept.
If the original conversion was done sympathetically and your planned conservatory is built using local materials you may have a chance of being accepted. The size of the conservatory may also be taken into consideration, so local knowledge and the advice of architects and builders may help you in your application.