My assassins can usually kill spies. Did you tell your assassin to kill someone during this turn?

Click on yer assassin and just like you can engage with negotions with diplomats with an assassin you can click to see whaty ou can do- sabtouge or assainate the person, it will give you your success rate i..e 78% and theres a round icon to the left of the scroll, near the bottom, that is for actually selecting the assassinate, then you cl;ick the tick button and yer sorted, yer assasin will attempt his mission.