His great-grandfather was the son of king George III and got the peerage in 1799 as the son of a monarch. As the title was inheritable in male-line, his father was the Duke of Cumberland and Teviotdale from 1878 (when his grandfather died), so as the son of the Duke of Cumberland and Teviotdale, he could be styled as 'prince EA of Cumberland and Teviotdale' (until 1917 when king George V took action by removing lots of privileges from his German relatives) - as well as prince of Hannover; just like for example nowadays William's children can be styled as 'of Wales' and Harry's children as 'of Sussex'.
King George III (1738-1820)
King Ernest Augustus of Hannover, 1st Duke of Cumberland and Teviotdale (1771-1851)
King George V of Hannover, 2nd Duke of Cumberland and Teviotdale (1819-1878)
Crown Prince Ernst August of Hannover, 3rd Duke of Cumberland and Teviotdale (1845-1923)
Prince Ernst August of Hannover (and of Cumberland and Teviotdale), Duke of Brunswick (1887 - 1953).