King's Gambit - Skellige
Area: Skellige
Location: Kael Trolde Keep
Quest Giver: Automatic upon completing The Lord of Undvik and Possession
Other Requirements: N/A
This quest is automatically given to you upon completing The Lord of Undvik quest as well as the Possession quest. Your actions during this quest determine who becomes the future king and play a large role on many future quests. Additionally, completing or failing King's Gambit will lock you out from completing Stranger in a Strange Land as well as The Cave of Dreams quests.
For this quest you'll need to first head over to Kaer Trolde Bridge which is the same location you had to meet Yennefer in the first Skellige quest, you should be able to use the Signpost and fast travel here. Follown Arnvald to the feast hall where you'll be able to do a few things before turning in the quest.
The first optional thing you're able to do (as pictured above) is to take Hjalmar up on his offer and fistfight the Vildkaarl. If you win, you'll get more EXP and Hjalmar's Sword. Once you defeat the first Vildkaarl you'll be able to speak to the one not wearing a shirt and challenge three of them in a row to a fight. Beating all three will get you a little bit more EXP.
That's all there is for optional content, head into the back room when you're ready to progress the quest forward and when you approach Crach there will be a scene. You'll receive EXP as well as another sword from Crach, your conversation will be interrupted by a commotion in the other room.
Geralt will bust into the other room and you'll find three really large bears tearing everyone to shreds. Use the Silver Sword as these are actually cursed ones and dispatch all of them to get more dialogue. You'll now have to make a decision between helping Cerys, Hjalmar or neither. If you choose to help neither of them then Svanrige will end up becoming the king instead of either Cerys or Hjalmar.
Choosing who to help also greatly alters the rest of the quest and how it is completed. As far as I could tell, there are no future quest lines that are dependant on who becomes king - only the aforementioned quests at the start of this guide.
Since there are two possible routes you can take for this quest, I have broken the rest of the guide into two parts. If you choose to help Hjalmar then skip to that part, if you choose to help Cerys then skip to that part. Hjalmar's part is much faster and has far less steps however Cerys' part will take you right by a Place of Power which'll save you time hunting it down later.
Help Cerys
After agreeing to help Cerys the first thing you'll need to do is inspect the corpse of one of the bears. Now inspect the container that held some mead in the center of the room right next to a corpse (pictured above). You'll acquire a scent that you'll have to follow the scent to a horn right next to the doorway leading out of the room.
The quest will update and you'll fill Cerys in on what you've found. Afterward go speak to Hjort, an old man outside. Cerys will lead you to him. Follow Cerys to the cellar after speaking with him and examine the barrels using your Witcher Senses. Find the one that smells of mushrooms and blood to trigger a scene. In the northern portion of the room you'll find some barrels stacked up that you'll have to use Aard on to clear the way (pictured below).
Follow the path back to the castle and make sure you collect the Ability Point from the Place of Power along the way. Back at the entrance to the cellar you'll find some foot prints in the mead that you will have to follow up the stairs and to a scrap of clothing hanging on the wall. Inspect it for more dialogue with Cerys.
She'll recognize who the tunic belongs to and will begin to rush to find Arnvald. While en route to Arnvald you'll be thrown into a scene of him escaping on horseback. You'll regain control of Geralt ontop of Roach and you'll have to chase Arnvald down and knock him off his horsey with an attack.
Help Hjalmar
If you choose to help Hjalmar you'll be teleported to the abandoned town of Fornhala far south of Kaer Trolde. Investigate the area Hjalmar points to up on the ledge to pick up a scent which you'll need to follow to some foot prints just up the hill. The foot prints will lead to a building at the top of the hill where a bearskin rug is covering up a hole in the floor.
Down in the cave you'll have to fight a man by the name of Halgrim who will transform into a bear half way through the fight. After defeating him you'll need to go further into the cave where you'll find a Druid by the name of Artis that will summon a bear during the fight which you'll want to ignore as he can keep ressurecting it.
Both paths will now converge back in Kaer Trolde. Depending on who you helped out the scene will play out slightly differently but they'll both end with the clan being cleared of all wrong doing. The king will ask you if you wish to fast travel to the Coronation ceremony, it's up to you if you'd like to or not. Either way, the quest Coronation is added to your quest log and King's Gambit is complete.