Prior to the start of the series the High Priest charges Thoros of Myr with the task of converting Robert Baratheon from worship of the Seven to the faith of R'hllor. The High Priest had foreseen Robert's ascension to the Iron Throne in the flames, as Thoros was already in King's Landing by the time the city was sacked and he was present when the bodies of Aegon and Rhaenys Targaryen, murdered by Ser Gregor Clegane, were presented to the new king.
In the books
In the A Song of Ice and Fire novels, the overall organizational structure of the faith of R'hllor has not been revealed. Individual cities have been said to possess a High Priest, such as High Priest Bennero in Volantis. Whether or not there is an overarching international leadership of the entire religion, however, the way the High Septon is the leader of the entire Faith of the Seven, is uncertain. It is possible that in the TV version Melisandre was simply referring to the High Priest in Myr, not an overall leader.
Thoros was himself not specified to have been sent to King's Landing by some sort of overall High Priest, but apparently by the local leaders of the Red Priesthood in Myr. In the TV series Thoros is said to have been sent to try to convert King Robert Baratheon, but this is a condensation from the books, in which Thoros was originally sent to King's Landing to try to convert King Aerys II Targaryen, due to his increasing obsession with fire. Thoros's preaching was not successful, but he remained at the royal court after Robert Baratheon seized the throne. He had even less luck preaching the religion to Robert, but he continued to hang around the royal court as one of Robert's drinking companions.