Renly Baratheon and Loras Tyrell

Renly Baratheon and Loras Tyrell have been in a stable romantic relationship for many years prior to the beginning of Season 1.

Renly Baratheon is the youngest brother of King Robert Baratheon and serves on his brother's Small Council as Master of Laws. Loras Tyrell is also one of the more prominent noblemen of the realm, as his father Mace Tyrell is the ruler of the Reach (most populous of the Seven Kingdoms).

In the books
Loras became Renly's squire some years ago and they have apparently been having an ongoing romantic relationship for some time.

The books implied that Loras and Renly were in a homosexual relationship, but didn't outright state it - simply due to the plot mechanics that they aren't POV narrators in the novels. Many of their scenes in the second novel are told from Catelyn's POV narration interacting with them, for example, and logically Catelyn wouldn't be present for scenes set in their private chambers. The TV series had more freedom for the camera to show events beyond the confines of POV characters from the novels, including what both Loras and his sister Margaery were doing "off screen". Thus many of the scenes between Renly, Loras, and/or Margaery didn't directly appear in the novels, though they probably "occurred" in some form, just "off-screen". Author George R.R. Martin did outright confirm when the TV series created romantic scenes for Renly and Loras in private for Season 1 that he fully intended them to be a romantic couple in the novels.

After Renly was killed, Loras took his body away and buried him in secret somewhere in the gardens of Storm's End so no one would ever disturb it (i.e. he was worried that Joffrey might order Renly's corpse desecrated as he tried to usurp the Iron Throne from him).

Following Renly's death, Loras becomes despondent. Eventually he joins the Kingsguard, in part to guard Margaery from Joffrey. When reminded that the Kingsguard swear never to marry or even love another but remain totally dedicated to service, Loras responds (without directly mentioning his love of Renly in public) that he is unconcerned, because once the sun of one's life has gone out, no candle can replace it (he knows he will never love again).

The TV series showed Loras having sex with the male prostitute Olyvar in Seasons 3 to 5 after Renly died, creating some consternation - writer Bryan Cogman later explained that the intent was just to show that Loras is "drowning his sorrows" with casual sex, as it were, and he is still deeply mourning his loss of Renly. To Cogman's deep regret, however, these scripted lines of dialogue were cut for time - they never intended to convey that Loras is "loving" again following his loss of Renly. While all of this wasn't directly stated on-screen due to time restraints they hoped it was at least still implied.