Following events at the Chamber of Eyes, the players will know that the captured slaves are in the possession of Duergar - but they won't know where these Duergar might be. So it's back to the Seven-Pillared Hall to look for clues.
The most obvious place to start looking is at the Grimmerzhul Trading Post, where the Duergar come to do their business with the residents of the Hall.
Thunderspire does its typical bait-and-switch here. It starts off describing the Trading Post by saying, "The Duergar here aren't interested in fighting but depending on the PCs' actions, a fight may break out."
So, great. This is a diplomacy encounter, then, right? The players are going to get the relevant information out of the Duergar by wit and deception, and they'll only end up in combat if they make a mess of the chatting?
Wrong. The Duergar "don't say much, answering in as few words as possible and being evasive if asked probing questions". Further, "the guards order the PCs to leave if [..] the characters press them about slave trading. If the PCs refuse to leave or if they try to enter another part of the trading post, the Duergar attack."
So it's a railroad. Once again, talking is only a prelude to the inevitable hitting-things-with-swords phase of the encounter. Just to reinforce the point, the encounter ends by reminding DMs that there's only three ways the players can find the Horned Hold - interrogating a captured duergar, ransacking the trading post, or (and I'll come to this option in another post) paying an exhorbitant price to the Hall's resident drow.
Combat in the Trading Post raises an ugly problem for continuity in Thunderspire Labyrinth. The Trading Post lies within the boundaries of the Seven-Pillared Hall, and its residents are largely peaceful members of that community. It can't be said that the Mages of Saruun are unaware of the Duergar propensity for slave-trading - they clearly permit the Duergar to do their business in full knowledge of the proclivities of their people. So when the players go deliberately causing trouble, why on Earth wouldn't Orontor descend on them with the full force of his magic and his animated statues?
One answer is that he needs their help to find his rogue brother Paldemar. But if the guardians of the Hall go making excuses for the players now, it significantly undermines their authority from that point forward. The supposed wrath of the Mages is what forces good-aligned surface dwellers to co-exist with Brugg and the other disreputable types dwelling in the hall. By ignoring this unprovoked attack on peaceful traders, Orontor (and the DM) are risking the start of a town-cleaning crusade , which at the very least is a significant diversion from the adventure that Thunderspire has planned.
As is often the case, none of this is a difficult problem to clean up for a confident DM, but it's another occasion of the module as-written being wilfully perverse, and holding out roleplaying with one hand while clubbing you with the combat-stick held in its other.