A quartermaster is a person assigned to supplying people of an organization.
During the 22nd century, Earth starships like the Enterprise NX had their own quartermasters, who oversaw the ship's supplies. (ENT: "Civilization", "Fortunate Son")
The Starfleet Quartermaster was responsible for Starfleet supplies like ration packs (ENT: "Countdown").
The USS Enterprise NCC-1701 had a Quartermaster. Kirk said to Spock (referring to Captain Christopher), "Why don't you have the quartermaster issue him something more suitable?". (TOS: "Tomorrow is Yesterday")
Klim Dokachin was the Zakdorn quartermaster of Surplus Depot Z15 in 2367. (TNG: "Unification I")
Starfleet Chief Edgar Willoughby was the quartermaster for the Bajoran sector in 2375. (DS9: "Treachery, Faith and the Great River")