After finishing chapter 6 I don't have new goals to achieve. Is this correct or am I missing something?

Chapter 6 is the last of the tutorial section of the game. After that you can progress in your own way. Near the bottom of the screen (in the town view) just above the chat box is a quest bar and tapping this will give you a list of the daily tasks to get rewards and main tasks that will be areas you can work on. But in general you can now build, upgrade research and progress however you want.

In addition to these tasks, the hourly challenges in the events list and the other events that come along in time (Clash of Provinces for example) at the best way to earn rewards to speed up your progress.