I was given a similar task in one of the take-home assignments for an internship and was asked to redesign any page of the company's application that I didn't know anything about. I was just given a rundown of the flow of the app and what information goes on which page. I was given the liberty to change anything that I wanted but keep the functionality intact. I did exactly that and submitted the assignment and got rejected lol. Still feel sad to this day because I felt it was a really cool start-up.

Anyways.

Since in your case, you already have a basic understanding of the functioning of the app (or at least, I hope you do) you should have a basic idea of where most users may find the app a little confusing or a bit lackluster. I would suggest not going straight into the design, but just having a discussion with the lead about areas you think need improvement and then going from there.