Surina doesn't work.
The Thunderspire Labyrinth developers obviously think she does. They give her half a page and a stat block, making her the most fleshed-out character in the Seven-Pillared Hall. But as printed, she's just not a success.
Surina is a female Dragonborn Warlock, on something of a crusade. She's apparently the veteran of past campaigns against gnolls and suchlike in other parts of the world, and she's brought her war with her into the Seven-Pillared Hall. The module describes her as agitating for aggressive action against "the evil factions within the Hall" (the duergar and drow) and she's engaged in an attempt to turn the Hall into a kind of armed base-camp for military expeditions into the Underdark.
Her story arc is a traditional tale of corruption. She's letting her zealotry guide her into some fundamentally bad decisions involving violence and intolerance, and eventually someone's going to get hurt as a result. It doesn't help that she's picked up an Imp companion somewhere who's giving her some mischievously terrible advice.
That's a great character, but it just doesn't fit Thunderspire Labyrinth. The players can't get involved in her story. The module has the players scheduled to fight the Duergar in Act 2, before they head off to the Horned Hold. If they get into a fight early, they're going to significantly complicate things later, and when it is time to take on the dwarves they don't need any encouragement.
On the flip side, the players aren't likely to want to stop her, either. She's right. The Duergar and Drow are vile, malevolent slavers who bring pain and misery to everyone they meet. If Surina announces an intention to declare war on the entire Underdark, the best the players can do is pat her on the back and say, "Go get 'em, tiger!"
Much like Brugg, Surina is ultimately an accessory character - to be used or ignored as your particular game demands - but the problem really is that she has an arc. If you want her to help the players when they attack the Duergar, or confront the players if they get too friendly with the bad guys, then it really works best if you introduce her early. On the other hand, if you do introduce her early, you're in danger of your players jumping straight on her Duergar-slaying bandwagon the moment they meet her and picking a fight they're not ready to win.
This is the problem with the Obvious Questgiver model of adventure design. Both Keep on the Shadowfell and Thunderspire Labyrinth are replete with random strangers who have tasks they'd like someone to do. So when a basically well-intentioned Dragonborn idly mentions that it'd be swell if someone murdered the entire Duergar race, players are all too likely to obligingly note it in their quest logs.