The Dragonlance campaign setting is coming to Dragonlance: Shadow of the Dragon Queen doesn't appear to be adding any. Dragonlance has lots of scope for new subclasses, which should make their way to D&D 5e.
The first time D&D fans learned of a possible Dragonlance revival was when an Unearthed Arcana article listed different races, backgrounds, and feats from the world of Krynn. These included some powerful new traits for characters to possess, as well as the amazing Lunar Magic subclass for sorcerers, though that was the extent of the new class and subclass options. The Knights of Solamnia and the Mages of High Sorcery are now relegated to Background status, even if they do offer some amazing abilities for characters.
Dragonlance: Shadow of the Dragon Queen is set during the War of the Lance era, which means that the Knights of Neraka have not been formed and the War of the Souls has yet to happen, so content relating to them likely won't appear in the book. There is still a lot of Dragonlance content from the older editions of D&D that can be adapted for 5e, especially ones related to the races of Krynn. Below are some of the Dragonlance subclasses that can be added to the latest edition of D&D.
The Kender Handler Is A Rogue Driven By Curiosity, Rather Than Gold
It has been confirmed that the kender are returning to D&D in the Dragonlance: Shadow of the Dragon Queen book, as they were featured in a previous Unearthed Arcana article where they later received a buff. It's rare for D&D to lock classes and subclasses behind races anymore, with even the elven Bladesinger class now available to all characters in D&D 5e, but the Handler might be one that deserves to stay exclusive to one race. The kender are the halfling equivalent in the world of Krynn, yet they are different in a number of ways, as they are motivated entirely by curiosity and a childlike appreciation of all things, which often get them in danger.
The Handler D&D subclass is the kender version of a rogue. The average kender would scoff at the idea of being a thief, as they aren't motivated by gold, nor do they actively seek bloodshed. Instead, the Handlers love to collect things they find interesting, even if they have no monetary worth. This leads to the Handler learning many of the skills of the rogue class, even though they don't appreciate the fact that they're often used for things that the races would find to be criminal. The Handler subclass for the rogue can have access to a number of abilities that let them snatch items in battle, and can spread their incredible luck among their party .
Gnome Tinkers Use Inventions (That Sometimes Work)
In the world of Krynn, the gnome race is known for its inventions. The gnomes are also known for their inventions rarely working and often blowing up in their face. D&D 5e has a class called the artificer, who specializes in using magic to bolster their equipment. In the old lore of Krynn, the only races that could use magic were humans, elves, and ogres, but this will likely be retconned in Dragonlance: Shadow of the Dragon Queen, as it would severely limit the character options available to players. As such, if the gnomes are Krynn are allowed to use magic, then they would make for perfect artificers, and the Tinker Gnome would be an ideal choice for them.
The Tinker Gnome class would specialize in creating overly-complicated devices that can be used to solve problems or take care of foes in battle. This D&D subclass could make for an interesting variation of the Wild Magic subclass for sorcerers, with their devices have a random chance of performing specific effects. The Tinker Gnome would need a few guaranteed moves, in order to make them a viable choice for players, which is why giving them the regular artificer spells is helpful for making them useful, while the inventions can be used to have some fun, and possibly succeed by accident.
Renegade Wizards Use Forbidden Magic (And Are Hunted As A Result)
The existing Dragonlance character backgrounds in D&D 5e cover the Mages of High Sorcery. In the world of Krynn, there is a vast and powerful order of mages, who belong to three specific groups: the black robes, the red robes, and the white robes. If a person wants to become a true mage in the eyes of the order, they must perform The Test, which is an incredibly deadly magical examination, that is tailor-made to play on the fears of everyone who takes it. Once someone completes The Test, they are free to study magic to their heart's content, though they must still abide by the laws of the order.
There are some in Krynn who reject the ideals of the order and become known as renegades. These mages study forbidden magic and often hide their true identity from others, as many mages will slay a renegade on the spot, or at least imprison them, so they can be judged by the rest of the order. There are lots of interesting stories told using renegade wizards in the Dragonlance novels and they have a place in D&D 5e.
The current Player's Handbook has several classes that don't exist in the world of Krynn and the renegades can be used as a way of including them. The Renegade Wizard is an easy subclass for the main Wizard class, but it's also a good option for the Warlock, as they make deals with powerful creatures in order to by the need to call on the three moons of Krynn for spells. Dragonlance: Shadow of the Dragon Queen is set during the opening of the War of the Lance, which means the heroes will need all of the help they can get in fighting the dragon armies. This means there's a role in the story for renegade wizards, while the subclass can be used to bring in abilities and spells that are normally not part of the world of Krynn.
Dragonlance: Shadow of the Dragon Queen and Dragonlance: Warriors of Krynn will launch in late 2022.