Mr. Ellison is the legal guardian of Miss Sophia Grey, which likely means they are related in some way. He and his wife never appear on the page, but are discussed at various junctures throughout the novel. Given the society in which they seem to move, it is likely that they keep a home in London.
Mrs. Jennings leads us to believe that Mrs. Ellison and Miss Grey do not get along and that, therefore, the Ellisons are very pleased to get Miss Grey off their hands when Willoughby expresses an interest. Later on, Colonel Brandon overhears Mrs. Ellison gossiping in Pall Mall about the engagement the day that the news breaks publicly.