"a better insight" is correct and usable in written English. You can use it when you want to refer to a better understanding of a certain topic or situation. For example, "Through research, I gained a better insight into the history of the city.".

The phrase 'to gain a better insight' is correct and usable in written English. You can use it when you want to express the idea of gaining an understanding of something. For example, "This research project will allow us to gain a better insight into the health benefits of eating a plant-based diet.".

This phrase can be used when you want to communicate that someone should gain a more comprehensive understanding of something. For example, "Studying the history of the company will give you a better insight into how it operates.".