Through her grandmother Mary Wynn, Priscilla Bertie was a descendant of the Welsh princely House of Aberffraw.

On 23 February 1779, she married Sir Peter Burrell (later 1st Baron Gwydyr) and they later had four children.

On 8 July 1779, her brother, Robert Bertie, 4th Duke of Ancaster and Kesteven, died of scarlet fever at the age of 22 and his dukedom passed to his uncle, but his barony of Willoughby de Eresby, as well as the office of Lord Great Chamberlain, went into abeyance between Priscilla and her sister, Lady Georgiana (later Marchioness of Cholmondeley).

On 17 March 1780, however, the abeyance of the barony was terminated in Priscilla's favour, as the elder sister.

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