Margaery’s age, at first – she’s sixteen for the bulk of ASoS, at least, meaning that she was quite possibly fourteen in the earliest parts of AGoT. The idea to marry her to Robert was probably floated when she was fourteen-fifteen. Don’t forget, either, that Renly’s twenty-one in AGoT and Loras sixteen. Neither of them are hugely experienced schemers.
And yes, the political situation did stall things. Jon Arryn’s death is not only a political event, but a personal matter for Robert; shoving Margaery at him when he’s trying to actually grieve for someone might come across a bit tacky and put Robert off. Likewise, interrupting Robert’s “I got my BFF back!” high might also go poorly. The royal progress to Winterfell and the Tourney of the Hand are both disruptive to court business as normal. Ned himself had to be factored in in terms of replacing Cersei. Then the Stark-Lannister feud kicked into a higher gear.
Until Renly had the marriage to Margaery ready to go, right then, Robert’s cooperation guaranteed, he didn’t have the pieces he needed. There wasn’t a great window for him to bring a sufficiently grown-up Margaery to court in AGoT, and so the plan ended up not happening.
I got the same ask, so I figured I’d add my contribution to the conversation here rather than having two threads as it were.
I don’t think Renly was “waiting,” per se. He was, in fact, carefully moving his plan into place:
- Already in Bran II of AGOT, we see Cersei naming Renly as one of her “ambitious” enemies, and saying “my husband grows more restless every day. Having Stark beside him will only make him worse. He’s still in love with the sister, the insipid little dead sixteen-year-old. How long till he decides to put me aside for some new Lyanna?”
- Then not long after Renly shows up in person, we see in Eddard VI him approaching Ned about Margaery: “Ned was not sure what to make of Renly, with all his friendly ways and easy smiles. A few days past, he had taken Ned aside to show him an exquisite rose gold locklet. Inside was a miniature painted in the vivid Myrish style, of a lovely young girl with doe’s eyes and a cascade of soft brown hair. Renly had seemed anxious to know if the girl reminded him of anyone, and when Ned had no answer but a shrug, he had seemed disappointed. The maid was Loras Tyrell’s sister Margaery, he’d confessed, but there were those who said she looked like Lyanna.” Clearly he’s trying to sound out Eddard about whether he can pitch Margaery as Lyanna come again as a hook for Robert’s interest.
- In the very next Eddard chapter, we see that Renly had been talking to Robert about Margaery as well, and that Robert is receptive: “Have you seen Mace Tyrell’s boy? The Knight of Flowers, they call him. Now there’s a son any man would be proud to own to. Last tourney, he dumped the Kingslayer on his golden rump, you ought to have seen the look on Cersei’s face. I laughed till my sides hurt. Renly says he has this sister, a maid of fourteen, lovely as a dawn …"
- Right after that, we see in Arya III that Renly has taken action to get Margaery to court, to put his plan into action: “The Knight of Flowers writes Highgarden, urging his lord father to send his sister to court. The girl is a maid of fourteen, sweet and beautiful and tractable, and Lord Renly and Ser Loras intend that Robert should bed her, wed her, and make a new queen.”
But then a series of events take place that radically alter Renly’s plan: Robert and Ned quarrel over the assassination of Daenerys so Eddard resigns and is then attacked by Jaime; a week later, Eddard is reappointed and Robert goes off on his fatal hunting trip.
These unexpected events meant that Renly ran out of time to bring Margaery to court and seduce Robert, so he shifts to trying to get Ned to mount an anti-Lannister coup, and then when that doesn’t work hightails it out of King’s Landing and goes for plan B instead.
But you could easily see things going another way – if Robert is a bit luckier in his duel with the boar and survives yet another sloppy assassination attempt, Margaery arrives at court just as Robert’s relations with the Lannisters reach the breaking point thanks to Jaime’s actions in King’s Landing and Tywin’s actions in the Riverlands, Renly springs Margaery on him at the opportune moment, and we’re off to the races.