A quartermaster was a person assigned to supplying people of an organization.
Upon his transfer from Enterprise to Columbia, Commander Charles Tucker III was advised by Captain Hernandez to see the quartermaster and get a new assignment patch for his uniform. (ENT: "Affliction")
The USS Enterprise had a quartermaster, also responsible for providing attire to crew members and guests. James T. Kirk said to Spock (referring to Captain Christopher), "Why don't you have the quartermaster issue him something more suitable?" (TOS: "Tomorrow is Yesterday")
In 2269, Spock requested a Vulcan desert soft-suit and boots, a small selection of street wear and carry bag, circa 8877 Vulcan years, for an expedition back in time. These supplies were issued by the quartermaster's wardrobe section. (TAS: "Yesteryear")