Like Clyde's therapist, Dr. Lopez, Gayle has yet to make a physical appearance in the show.
She is first mentioned in "Get the Message", in which Clyde uses one of her perfumes.
In "Along Came a Sister", Clyde brings Lincoln a casserole that she made (or one that Clyde made from a recipe that belonged to her) to Frank's "funeral", telling him that she believes there's no greater comfort in times of grief than casserole.
In "Lincoln Loud: Girl Guru", Clyde tells Lincoln that his Nana believes that you shouldn't trust people who don't like chocolate while they were attempting to make chocolate pies for a school project.
In "Snow Way Down", it is revealed that Clyde's Nana's name is Gayle.