Gelmir was a Grey-elven personal name, mentioned on two occasions during the First Age (both times regarding Elves of the House of Finarfin).
In the first instance, Gelmir was the son of Guilin of Nargothrond. He was captured during the Dagor Bragollach by Morgoth, mutilated, blinded, and at Morgoth’s command, put to death outside the walls of Eithel Sirion (as a challenge to those defending it; among them, Gelmir’s brother Gwindor). It was this act that began the great battle of the Nirnaeth Arnoediad.
In the second case, Gelmir was an Elf of the people of Angrod and the companion of Arminas, who came to Nargothrond to deliver a message of warning from Círdan of the Havens shortly before the sack of Nargothrond.