Elmo is only mentioned in the Unfinished Tales in discussions on Galadriel and Celeborn. Because Celeborn is in The Silmarillion presented as a "kinsman of Thingol", Tolkien wished to develop this family link. One of his solutions was to establish Celeborn as the grandson of Elmo, a non-important brother of Elwë who remained behind when Elwë was lost, becoming one of the Sindar of Doriath.
It therefore remains unsure if Elmo would have remained in the Middle-earth canon, as his position in the royal Sindarin family tree disappeared. Slightly later writings however make Círdan a descendant of Elmo, making him a kinsman to Thingol (and Celeborn). Certain is that Círdan had silver hair, a trait which otherwise only ran in Elwë and Olwë's family line, and Círdan's original name Nowë is similar to Elwë and Olwë.