Most rights of common are attached to a property (e.g. farmhouse). Rights of common in gross are different because they are deeds which allow the person who has the deed to exercise that right of common. By attaching the right of common in gross to a property it will cease to be a right of common in gross and will be permanently attached to that property. The people who can apply are the person who owns the right of common in gross or the land to which the right of common will be attached (e.g. farmhouse). Often they will be the same person.
This relates to section 10 of the Commons Act 2006.