To get to the next chapter, you need to open the big gates. To do so, a certain Collector Level is required. The level you need corresponds to the number of a chapter you're going to open (e.g., if you want to open chapter 3, you need to reach Collector Level 3).
Your current Collector Level is indicated at the top of the screen.

If you notice any problems with your Collector Level, please contact our support team.