This definition is based on traditional Maori concepts.
The role of a kaumatua is to share, teach and guide the up and coming generations in the history, tikanga and te reo of their people, with wisdom, to ensure that the mana of the whanau, hapu and iwi are maintained.
Formal "lessons" do not need to be arranged, as a kaumatua would have been taught by their kaumatua over the years through korero and attending different events. It is by this same style that a kaumatua passes on what they know.
A kaumatua is not necessarily the person who speaks on the marae or who does the karanga for if that is not their skill, by doing so could bring the mana of the marae down.
A kaumatua usually has a specialty field, ie: whakapapa (genealogy), history, tikanga etc. However, they will also know people who are specialists in the areas that they are not, and can call on them when the need arises.