I discussed the protocol that would arise if Prince Harry became engaged to actress Meghan Markle in a recent interview with Hello! Magazine. The Royal Marriages act of 1772 required all descendants of King George II (with the exception of the descendants of princesses who married foreigners) to receive the permission of the monarch in order to contract a legal marriage.
Since the succession reforms of 2015, only the first six people in the line of succession require the permission of the monarch to marry. As Prince Harry is currently 5th in line to the throne, after his father Prince Charles, older brother Prince William and nephew and niece, Prince George and Princess Charlotte, he will need the permission of his grandmother, Queen Elizabeth II, to marry.