Gore was the eldest son of William Gore and his wife Lady Mary Compton, daughter of George Compton, 4th Earl of Northampton. He matriculated at Christ Church, Oxford on 12 July 1729, aged 18. In 1739 he succeeded to Tring Park on the death of his father. He was responsible for diverting the main Aylesbury to Berkhamsted road from a course through the park, which took it straight past the front door of Tring Park Mansion, to its present route following considerably flatter terrain further north. He married Ellen Humfreys, daughter of Sir William Humfreys, 1st Baronet, of London, on 3 December 1741.
