You have to do a series of lengthy side quests to trigger the "Reason of State" side quest at the very end of the game. During "Reason of State" you will then automatically assassinate King Radovid as part of the quest.
If you miss one of the required side quests before going to the Isle of Mists you cannot trigger "Reason of State" anymore. If you make a wrong dialogue choice during the "Blindingly Obvious" main story quest you will miss it, too. Be sure to always choose the first dialogue option at the end of this quest when talking to Dijkstra and Philippa.