The following data is extracted from Hunter Family History.
ROBERT HUNTER: (d. 1734), Governor of New York and Jamaica, belonged to the family of Hunter of Hunterstin, Ayrshire (See Burke, "Landed Gentry," 1886 ed.) Paterson describes him as one of the children of James Hunter, who was a son of the laird of that ilk, and married Margaret, daughter of the Rev. John Spalding of Dreghorn. It appears probable that Hunter was the Robert Hunter, esquire, appointed Mayor of Brigadier-General Charles Ross's dragoons (5th royal Irish Dragoons) on 13 April 1698. Hunter was appointed Governor of New York, and sailed with the refugees early in 1710. In November of the same year he reported that the refugees were settled on the banks of the Hudson, close to the great pine woods, and that 15,000 Pounds a year for the next two years was all that was needed for the success of the great project. He promised that the colonies would supply tar enough for the English Navy forever if sufficient hands were employed. Orphans, he wrote, had been made over to those who would maintain and educate them. Each person's account was kept separate, as each would have to repay by their labour what they then received. He prophesied that their numbers would increase, as they were very healthy. He died in Jamaica on 31 March 1734. By his will, probated in November 1734, he left considerable property at Chertsey (including the patronage of the living) to his son Thomas Orby-Hunter (d. 1769), M.P. for Winchilsea, from whom descended the family of Orby-Hunter (on condition of his not contracting a certain marriage), together with 5,000 Pounds to his daughter Katherine, wife of William Sloper, and fortunes to his daughters Henrietta and Charlotte. He also mentions a debt of 21,000 Pounds due from the crown for the subsistence of the colonists of the palatine in New York, which "had been acknowledged by Mr. Harvey and the treasury, but never paid." Hunter became a member of the Spalding Society in 1726. Most biographers, relying on Swift, describe Hunter as the author of the "Letter Concerning Enthusiasm," which was written by Shaftesbury, and of which the original is in the "Shaftesbury Papers" in the Public Record Office.
Source: Hunter Family History