Koryū (古流) can be translated as old school (or tradition). The term is usually reserved for Japanese martial art schools that are older than 1868 (i.e. before the Meiji Restoration).
In Japan there are two prestigious classical martial art organizations: the “Nihon Kobudo Kyokai” and the “Nihon Kobudo Shinkokai”. Most well-recognized old schools are member of at least one (sometimes both) associations. Nevertheless a small number of Koryū have chosen not to be member of either organizations.
Hontai Yōshin Ryū is a member of the “Nihon Kobudo Kyokai” (belonging to the Nihon Budokan).
More information on Koryū can be found in the following article: