A hypochondriac, Telfer habitually avoided assignment on away missions by getting The Doctor to declare him unwell and thus unfit for away mission duty. Commander Chakotay, who, as Voyager's first officer, had the duty of rostering crew duty assignments, put it very succinctly when he once remarked with annoyance that Telfer never went on away missions because he "always seems to get a note from his doctor."
Among his crewmates, he was especially close to a Bajoran crewman named Tal Celes. He frequently helped her perform her work as an astrometrics sensor analyst, which she found very difficult due to competence issues.
In 2376, an efficiency analysis of all of the ship's departments was conducted by the head of the astrometrics department, Seven of Nine. The results, presented by Seven in a senior staff briefing, noted Telfer, as well as Celes and another crewman, Mortimer Harren, as being especially detrimental to the ship's operational efficiency. Telfer was specified due to his habit of visiting Sickbay once a week and wasting The Doctor's time and Sickbay's resources with his hypochondria.
The ship's captain, Kathryn Janeway, decided to take the three crewmen on an away mission to survey a Class T cluster, in hopes of inspiring them to better their performance. She assigned Telfer the task of looking for any signs of life that may have been present, as unlikely as this was. Telfer, as per his habit, tried to get The Doctor to declare him medically unfit, but this time, The Doctor refused (possibly due to a direct order from Captain Janeway to do so).
The mission proceeded well at first. Then their vessel, the Delta Flyer, was struck by an unknown force which was thought to be a dark matter proto-comet, rendering the vessel unable to attain warp speed, thus stranding the crew several light years from Voyager. Telfer was then transported away by what were thought to be dark matter lifeforms.
He was returned soon after with one of the organisms inside his body, which caused him intense pain. The organism later left him, making an agonizing exit from his body via his neck, after which it was killed by Harren. However, after the whole experience, Telfer found, to his great surprise, that he had been cured of his hypochondria.
Later on, when a swarm of the creatures was advancing on the Flyer, Telfer joined Celes in refusing to follow Captain Janeway's order to leave in the escape pods and seek shelter on a nearby planet, leaving Janeway to face the aliens alone. Harren followed the captain's order, but then suddenly decided to 'play hero' by piloting his pod toward the creatures to provide a distraction for the Flyer to escape. Telfer was able to beam him and the pod back aboard, on Janeway's order.
He was last seen lying unconscious in Voyager's sickbay, along with Janeway and the other two away team members, after Voyager had picked up the Flyer's distress signal and retrieved the shuttlecraft. (VOY: "Good Shepherd")