Tarquin was a humanoid alien with telepathic abilities. He was encountered by Enterprise 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 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 Tarquin's species is 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 and coerce her by threatening Enterprise.
As a parting gift, Tarquin gave Hoshi the coordinates of a colony where part of the Xindi superweapon was being constructed. (ENT: "Exile")