The term 'Local Authority EDICT' can be broken down into two parts: 'Local Authority' and 'EDICT'. A local authority is a public administrative body responsible for local government in a specific area. An EDICT is an authoritative proclamation, especially one issued by a sovereign or government. Therefore, a Local Authority EDICT is an authoritative proclamation issued by a local government. The crossword solution for this term is 'BYLAW', which is a law or rule made by a local authority.