Destiny: The Taken King includes a new subclass for the Titan, but you will have to complete some tasks before accessing to it. Mainly, there’s a quest to accomplished to get the Sunbreaker, and its name is obviously The Sunbreakers Challenge. Complete the first part of The Taken King questline, then go to the Tower and get the quest. Bear in mind this is a solo only mission and you will have to go to Venus in order to do it.
Follow the marker to the mercenary clan you are searching for, The Sunbreakers. Once you get to the marker, deploy you ghost and you will get a new way marker. Go up the stairs and out the door and you will find some enemies.
At the end of the path you will run into an Elite Hydra you will have to kill for the first part of the quest. Use your ultimate if you need to and your heavy weapon to make quick work of it.
The next part is where you will have to light a forge and get the Sunbreaker class. Once you get it, use the Subreaker skills to get 100% rid of all the enemies on field. End the quest to fully unlock the class, and get back to the Tower for some EXP and Armor.