Rhaenyra's first notable relationship is with Ser Criston Cole, her sworn shield and a member of the Kingsguard, making any relationship between them utterly forbidden. In the book, the exact nature of Rhaenyra and Criston's relationship is unknown, and different sources report different rumours. The general gist seems to be that she had a crush on him for years. One source suggests she convinces Daemon to teach her how to seduce Criston but that Criston then rejects her. Another source suggests Criston asks her to elope with him, but she rejects him as unsuitable for a princess.
Whatever the reason, a rift between them develops, which is worsened when Criston kills the closest friend of Rhaenyra's new husband, Laenor, at their wedding tourney. During the Dance of the Dragons, Criston sides with Aegon and Alicent.
"House of the Dragon" offers more clarity on what really happened between Criston and Rhaenyra. After nearly hooking up with Daemon at a brothel, Rhaenyra returns to the Red Keep and, instead, convinces Criston to sleep with her. She's disappointed when he returns the next day and tries to put the night behind them, crushing her romantic hopes and foreshadowing the rift that is fast approaching.