 He was succeeded in the earldom of Hopetoun by his half-brother, John Hope.The claim to the earldom of Annandale and Hartfell passed to his eldest daughter Lady Anne, who married William Johnstone Hope.His daughter Georgiana Hope-Johnstone (d. 1797) married Andrew Cochrane, youngest son of Thomas Cochrane, 8th Earl of Dundonald, in 1793; Cochrane added "Johnstone" to his name to become Andrew Cochrane-Johnstone.