A new event will let you know that Linzi wants to talk to you. Head to the throne room, to find out that your throne is missing! The “Runaway Throne” quest will officially start, have few words with the people Linzi advised you to talk to, then head back to the throne room to start the Tracking the Throne Thief project, it takes 60 days to complete, so you might want to send your Minister for the job asap. Alternatively, you might stumble into the Goblin Merchant in a random encounter during travels, but there really is no guaranteed about where or when. Talk to the goblin, he will offer you to buy back the throne. Don't fall for it, pick the “I can do without this junk. I have to go.” option. He will again attempt to convince you. Don't accept, pick “For this piece of junk? What should I do with it? Carry it on my back and entertain people? You keep it!”. He will attempt to strike a deal by offering it for cheaper. Again, don't fall for it, choose “You think I am an idiot?! I'll find another chair, newer and shinier! And you can keep dragging this thing around - you'll be the fool of goblins everywhere!”. He will offer it for free, and I know that sounds tempting, but don't accept it! Now congrats, you just made a goblin cry, and got your throne back.
Credit to Starsong for their
guide.