Apart from this one document, hardly anything is known about Patmos in the Hellenistic period. It is rarely mentioned by ancient authors. For a summary of the little that is known about the island in ancient times, see the Princeton Encyclopedia of Classical Sites.
A commentary on this inscription with a French translation, by O. Curty, has recently been published in the Journal of Epigraphic Studies (2019). Some details about the technical terms and official titles are provided by the Inventory of Ancient Associations.
In the year of Sopolis, in the month of Artemision, it was resolved by the association {koinon} of the lampadistai in Patmos and those who share in the anointing-oil: since Hegemandros son of Menekrates has continually behaved with piety towards the gods, and has acted nobly towards his kinsmen and the citizens, providing assistance to them from an early age, both in common and individually to each one of them; and also he has served as gymnasiarch seven times, and has served as lampadarch, and has won the long race, and has done all this in this 10 in a manner that befits both himself and us; and, being appointed chrysonomos {"treasurer"} of the lampadistai, he protects the money and takes care of all other matters; and now he has pledged that he will dedicate a stone statue of Hermes and he will provide two hundred drachmas, so that they can be put out for interest; and he has pledged that, for as long as he lives, out of his own resources he will both perform the sacrifices and manage the Hermaia; therefore it is resolved that Hegemandros shall be praised for the good attitude that he has; and that the lampadistai {"torch-runners"} and the aleiphomenoi {"those who are anointed for exercise"} shall crown Hegemandros with a golden crown 20 of five Alexandrian staters, and with a
painted portrait; and that an eponymous day shall be observed in honour of him; and that the priesthood [? of Hermes shall belong] to Hegemandros; and if . . .
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