Tarquin was a humanoid alien with telepathic abilities and some undefined power or technology allowing him to shut down the power supplies of starships. He was encountered by Enterprise NX-01 in October of 2153.
Born sometime prior to the 1750s, Tarquin was discovered to have telepathic abilities. As such abilities were considered threatening on his homeworld, he was exiled to his own planet to live out the rest of his days in isolation.
Tarquin's telepathic ability had a number of different aspects. According to him, every artifact has, imprinted on it, traces of the people who made and used it. Tarquin could read those imprints. He could also connect with certain minds on a very deep level, being able to read their every thought. Very few people have minds this sensitive; those who did included Morianna Taal and Hoshi Sato. His telepathy was limited in range; as a going-away present, his family presented him with an egg-shaped object he could use to extend it.
Lonely, Tarquin began telepathically searching for someone he could share his exile with. Morianna Taal was the first, but as his species was very long-lived, she died while he continued to live. He searched for another companion; he had had four in total by the time the last one died before the 2050s. He said that sometimes he did not know what was worse: living alone or burying his companions.
In 2153, Tarquin detected Hoshi Sato aboard Enterprise as it traveled through the Delphic Expanse. Her mind was of the right type for him to connect to, and he began to monitor her thoughts for several days. Eventually, he made full telepathic contact with her, inviting her to join him on his planet in exchange for giving the Enterprise crew information on the Xindi.
Sato stayed with Tarquin for several days while Enterprise investigated a Delphic Expanse sphere. During that time, she learned of his succession of companions and that he wanted her to become one. Sato refused, and foiled his attempts to telepathically trick her into staying. Once she saw through his ruse, he tried and failed to coerce her by threatening Enterprise, shutting down all power and systems on the vessel.
In the final draft script of "Exile", Tarquin's Human appearance was described as "an attractive human man." A note in the script also pointed out, "The same actor will play Tarquin as a human and an alien." Tarquin in his true appearance was scripted to be "a hulking, grotesque creature."
Also in the final draft script of "Exile", Tarquin was described as having had five companions prior to meeting Hoshi Sato, with the graves of all five at his sanctuary. However, this quantity was clearly reduced to four companions and graves.
Star Trek: Enterprise co-creator and Executive Producer Brannon Braga was pleased with how Tarquin is portrayed in the episode "Exile". "There's just something interesting about a lonely alien who's captivated by Hoshi's ability to communicate," Braga remarked. "The alien's interest in her helped elucidate what makes Hoshi interesting as a character [....] It was also interesting to use the telepathic alien to help us get some crucial information about the Xindi." (Star Trek: Communicator issue 151, p. 29)