The Council Meeting Serves a Number of Different Purposes
In addition to (1) providing new players with a summary of what was important in the previous module, the first Council Meeting serves as (2) an introduction to the various factions involved in the story. Unless your group really likes conversing with NPC's or already has significant background knowledge of organizations within the Forgotten Realms setting, the sheer number of possible interactions is going to be overwhelming, since this is the first scene. Rise of Tiamat lists five factions present at the first Council Meeting and ten named NPCs that are likely to speak at some point. On the other hand, for much of the adventure as a whole, the PCs will be far from Waterdeep and the Council meetings, and will thus have few chances to interact with these NPCs again. Therefore, the NPCs that get the most 'onstage time' at the first Council meeting should be those the DM sees as being the ones that are likely to be sources of continued interaction with the party; either because they are already important in the backstories or adventure hooks of the PC's, or because those are the factions to which the PC's will likely gravitate or with which they will interact most. There are a number of different factions and NPCs who can legitimately summarize the events of Hoard of the Dragon Queen for the PC's, but by choosing the ones the party is likely to re-encounter, the DM can do double duty with them.
Another use of of the HotDQ summary is (3) to have the players appreciate the perspectives of the different factions; as someone is relating an account of what the previous heroes did, the different factions can express their approval or disapproval, signaling to players what the factions are like.
Finally, the reaction of the Council delegates as a whole can be used (4) to guide new players in the playstyle and genre expectations of the DM. By describing the first set of heroes as clever (or too clever), sneaky (or cowardly), bold (or foolhardy), powerful (or incautious), etc, and having the NPC's present react to those descriptions, the GM can preview for the players what actions are likely to meet with what consequences in the upcoming adventure.
From Rise of Tiamat
Once introductions are made, Dagult Neverember summarizes the situation if the adventurers did not play through Hoard of the Dragon Queen. This includes the plan to summon Tiamat, increased dragon raids led by the cult, the treasure collection system, the crash or capture of Skyreach Castle, and the importance of the wyrmspeakers and dragon masks to the cult.
For what follows, each episode of Hoard of the Dragon Queen is summarized with what the previous heroes did, what is important that the current players learn, and who at the council could narrate the information.
Episodes 1 and 2: Greenest in Flames / The Raider's Camp
The heroes happened upon the town of Greenest at the time of a cultist attack. The cultist army included a blue dragon [increased dragon raids led by the cult] as well as numerous foot troops. The cultists largely ignored the keep in favor of looting the town [the treasure collection system]. The heroes snuck into the cultists' camp and rescued a Harpers' agent.
The Lord's Alliance: As the civil leader of the town, Governor Nighthill is likely a member of the Lord's Alliance. Lord Dagult could narrate this part of the tale, as reported to him by the governor.
The Harpers / The Order of the Gauntlet The monk Leosin Erlanthar is a member of the Harpers but is a comrade and confidant of Ontharr Frume, the lead delegate of the Order of the Gauntlet. Either Ontharr (for the Order of the Gauntlet) or Lady Remelia Haventree (for the Harpers) could narrate this part of the tale, as described to them by Leosin. [Note that Leosin plays a role in Rise of Tiamat but does not actually attend the Council meeting. He also is described as having researched dragon lore extensively. These two things indicate that the Harpers don't want to draw attention to him as an asset, so likely the story would be related as what was learned 'from a Harper agent' rather than specifically naming him.]
Episode 3: The Dragon Hatchery
After the cultist army withdrew, the heroes investigated their campsite and found underground chambers for breeding drakes, and one with dragon eggs [increased dragon raids led by the cult]
This episode can be recounted by any of the same people as Episodes 1 and 2
Options: The heroes were presented with the option of recovering or destroying three black dragon eggs. Strictly speaking, a DM starting with RoT would not have to specify what happened to them. However, announcing one of the options (as what did happen) at the Council meeting will allow the DM to then describe how the different factions react to the news (guided by the the Council Scorecard included in RoT).
Episodes 4 and 5 On the Road / Construction Ahead
The cultists disguised their looted treasure as a merchant caravan [the treasure collection system]. The heroes traveled to Elturel, then Baldur's Gate, where they joined the caravan in disguise. En route to Waterdeep they learned that the cultists are being aided by the Red Wizards of Thay. From Waterdeep they set out ostensibly for Neverwinter.
Since the heroes met Leosin and Ontharr in Elturell, the first part of this section could be narrated by The Harpers or the Gauntlet as in Episodes 1-3, but they would not necessarily know any details about the trip to Waterdeep. Since Lord Dagult is also Lord Protector of Neverwinter, he would reasonably be watching over any caravans headed that way and would be the most logical member of the Council to have interacted with the heroes at this point.
In the caravan with the heroes was an agent of the Zhentarim. Note that RoT as written does not call for the Zhentarim to be noticed until the second Council meeting, but if a DM wanted to introduce this faction at the first Council meeting, then having their delegate relate this section of the story, especially the discovery of the Red Wizard, would be the natural place to do so.
Episode 6: Castle Naerytar
The heroes follow the loot off the caravan trail, through the Mere of Dead Men, and to the ruins of Castle Naerytar, where the cult is served by a black dragon [increased dragon raids led by the cult]. The treasure is then carried through a magical teleportation portal [the treasure collection system].
It is not immediately clear from this point of the story forward how the heroes would have gotten word back to the Council of their doings, especially if the DM is assuming that they died in the crash of the Skycastle. The DM could posit that they made contact with an Emerald Enclave agent in the mere if they wish to spotlight this faction.
At this point the heroes would be fifth level, so the DM could also assume that they were provided with a sending spell or scrolls by Dagult in Waterdeep.
Episode 7: Hunting Lodge
The heroes followed the treasure through the magical portal to a safehouse near Parnast. They learned that the highest ranking members of the cult are called wyrmspeakers, and that each of the five has one of the dragon masks [the importance of the wyrmspeakers and dragon masks to the cult]. They also learned that the ultimate goal of the cult is the summoning of Tiamat from the Hells through a magical ritual [the plan to summon Tiamat]
Again, absent magical communication, it is unclear how the now-deceased characters would have conveyed this information back to the Council.
Episode 8: Castle in the Clouds
The heroes followed the treasure aboard a flying castle provided by an uneasy alliance that the cultists have with Giantkind. The castle was defended by a white dragon [increased dragon raids led by the cult]. Rather than allow the castle to be used to transport the treasure to the location of the summoning ritual, the heroes gave their lives to crash the castle and kill everyone aboard [the treasure collection system, the crash or capture of Skyreach Castle].
Again, absent magical communication, it is unclear how the now-deceased characters would have conveyed this information back to the Council.