Harry and Prince William have a close-knit circle of friends, all of whom have been vetted as trustworthy allies. Harry's girlfriend would also be expected to keep her lips shut on anything to do with their royal romance, including never talking about personal details to friends outside of the circle of trust who could pass along that information to the press. Chelsy never spoke about her long romance with Harry and has remained tight-lipped about any details to this day. (This is probably why Chelsy is still close to Harry and his circle of friends.) Cressida, meanwhile, doesn't strike us as the gossip type, especially since she is already such close friends with Princess Eugenie, Harry's cousin.
In short — be prepared to keep quiet, shed gossips from your group of friends, and don't forget to delete your Facebook, Twitter, Instagram, and all other social media accounts.