William was of Orange, not Hanover - that was George I.

William III & II came in as half of William and Mary, but it was his wife Mary II who was the heir. They died without issue, leaving the throne to Anne, Mary II's sister. There was no directly succeeding Stadtholder in the Netherlands.

Anne also died without issue, bring the Stuart dynasty to an end, and the entry of the Hanoverians with George I. This was a personal union (i.e. one monarch over two countries, not a single country). That came to an end when William IV died. Victoria could not inherit Hanover as it had Salic law (male inheritance only), so Hanover passed to her uncle, who became King Ernest Augustus I of Hanover.

The laws of succession for Hanover did not recognize female claimants. So after William IV it went to his brother instead of Victoria. To be later gobbled up by Prussia.

George I was never King of Hannover he was Elector of Hannover. The Elector or Kurfürst in German was a prince who together with other Electors elected the Holy Roman Emperor since the golden bull in the 14th century.

William of Orange was never King of Hanover; you're thinking of the Hanover dynasty that ruled Great Britain and Hanover simultaneously until Queen Victoria took the throne.

You should know that the current royal family is not descended from William of Orange. William ruled alongside Queen Mary II, whose sister Anne succeeded the throne afterwards, uniting England and Scotland into Great Britain.

Queen Elizabeth II isn't ruler of Hanover, either. Great Britain and Hanover went their separate ways after the accession of Queen Victoria. The United Kingdom follows male-preference cognatic primogeniture, where a daughter can inherit a throne if she has no brothers. Hanover instead followed agnatic primogeniture which excludes women entirely from inheriting a throne. The throne of Hanover passed to the Duke of Cumberland, Victoria's uncle, and it stayed in his line until Hanover was annexed by Prussia during the unification of Germany.

William of Orange (William III) has no descendants. During the so-called Glorious Revolution, he and his wife (Mary II, who was also his first cousin), supplanted James II & VII (her father, his uncle) and were co-sovereigns. In order to assure that England, Scotland, and Ireland would have a Protestant monarch, the succession would first devolve to joint descendants of William and Mary, then Anne (Mary's sister) and her descendants, and then the descendants of William (if any) not of his union with Mary. Mary, William, and Anne all died without living children or descendants.

Before William's death, the Act of Settlement (1701) was passed in order to clarify the succession to the throne. After Anne and descendants, the throne would pass to the descendants of Sophia, Countess Palatine of the Rhine and Duchess of Bavaria, Dowager Electress of Hanover. Sophia was a granddaughter of James I & VI and the nearest non-Catholic in the traditional line of succession. She was also much older than Anne but had living children.

William III died in 1702. Sophia died shortly before Anne in 1714. Therefore, Sophia's son, George Louis, Elector of Hanover, assumed the thrones of Great Britain and Ireland as next in line.

William IV was the last king of both the United Kingdom and Hanover, which became a kingdom in 1815. With his death, the United Kingdom passed to Victoria (the United Kingdom allows females to succeed when they have no brothers) and Hanover passed to her late father's next youngest brother. Thus, the personal union which came into being in 1714 ended in 1837. There were attempts to marry Victoria to her cousin the Crown Prince of Hanover but she preferred a cousin from her mother's side of the family, Albert of Saxe-Coburg and Gotha, instead.