 Elizabeth married the Royal Navy officer William Henry Shirreff.Murray had an electoral interest in Peeblesshire, where his older brother Alexander had been returned at a by-election in 1783, with the support of the dominant interests of the Duke of Queensberry and James Montgomery.Alexander stood down at the 1784 general election in expectation of succeeding his uncle George to become the 7th Lord Elibank, and David was elected unopposed in his place.