Rank is important in Riders Republic, not just because it tells other players how cool you are but also because it unlocks new gear and events for you. To rank up as quickly as possible, you will want to complete events and the specific challenges within the event.
Simply completing an event will award you a minimum of one star, but completing the optional objectives in the event will reward you with more. These additional stars could be one for easier objectives or as many as nine for more difficult challenges.
The types of challenges vary and will be themed for the event. For instance, a bike race may require to you finish the race with a specific bike. These kinds of challenges require you to have the bike and have it equipped. Other challenges may ask you to score a certain number of points or even to cross the finish line while falling.
There are other ways to collect stars and rank up such as finding relics and landmarks, but these will only award you one star. So to rank up quickly, you will want to do as many events as possible and complete their objectives. If you don't complete the objectives, you can retry the event as many times as you want to get the most stars.