According to one source, "There is not a Y-DNA signature publically identified for the Hannoverian lineage. However, there are a number of living persons whose genealogies link them to this lineage. For instance, the living male descendants of Ernst August von Hannover (1914-1987) are good candidates for testing."
http://www.surnamedna.com/?articles=y-dna-of-the-british-monarchy
I hope we'll get this one soon.