You have to do a series of length side quests to trigger the "Reason of State" side quest at the 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 question 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.
The necessary quests are all found in Novirgrad. They are as follows:
1. Redania's Most Wanted
2. An Eye for an Eye
3. A Matter of Life and Death
4. Now or Never
5. A deadly plot
6. Reason of State
7. [Main Quest] Blindingly Obvious
Be sure to do them as soon as they become available to you. The first four start automatically as part of the main story (track them in your side quests). A Deadly Plot becomes available immediately after doing the previous mission Now or Never for Triss. The last two will then trigger automatically