The British Officer who was a representative of the Governor General and who lived in a State which was not under direct British rule was called:

A Resident, or in full Resident Minister, is a government official required to take up permanent residence in another country. Instead of being a representative to a single ruler, a Resident could be posted to more than one native state, or to a grouping of states which the European power decided for its convenience. This could create an artificial geographical unit, as in Residency X in some parts of the British Indian Empire.