She had four brothers including Henry Pelham-Clinton, 6th Duke of Newcastle-under-Lyne, and Lord Arthur Clinton (who was involved in the 1870 Boulton and Park scandal).
Her childhood was blighted by her parents' divorce in 1850, following the scandal when her mother eloped with her lover, Lord Walpole, by whom she had an illegitimate son, Horatio.
On 25 January 1858, Lady Susan stood as one of the bridesmaids to Victoria, Princess Royal, at her wedding to Emperor Frederick III at St James's Palace.
Susan married Lord Adolphus Vane-Tempest (2 July 1825 – 11 June 1864) on 23 April 1860, several weeks after her twenty-first birthday.
During DNA searching for the Romanov Family, an Australian man discovered a connection to Susan and to Queen Elizabeth II.