I'll try to avoid getting overly philosophical, just describing roughly what I did from blue to purple.

Familiarize yourself with as much of the game as you can and start developing paths to and from positions (Stephan Kesting's free BJJ roadmap can be a good place to start).

Always have two things you are working on.

One, trust your instructor, pay close attention, make notes if you want/can, follow their tutoring.

Two, have something you are very interested in and want to work on that is practical for your game (not some crazy sub or transition that you'd never practically get into at your current stage). This doesn't have to be complicated but should be a deep dive and suite you personally. I spent weeks or months on each one of these things for myself, with much help from YouTube, occasionally I'll try to avoid getting overly philosophical by just describing roughly what I did from blue to purple.

Familiarize yourself with as much of the game as you can and start developing paths to and from positions (Stephan Kesting's free BJJ roadmap can be a good place to start).

Always have two things you are working on.

One, trust your instructor, pay close attention, make notes if you want/can, follow their tutoring.

Two, have something you are very interested in and want to work on that is practical for your game (not some crazy sub or transition that you'd never practically get into at your current stage). This doesn't have to be complicated but should be a deep dive and suite you personally. I spent weeks or months on each one of these things for myself, with much help from YouTube, occasionally from instructionals, and of course training partners and coach, usually after regular class was over. This included techniques like how to finish an arm triangle without cranking the neck, how to solidly get to and finishing an arm triangle under high resistance, how to get and finish a leg triangle under high resistance etc. Whatever you find yourself struggling with something or you find something interesting or something that might fit your body well.

Compete occasionally, not too often so that you have time to cultivate new knowledge/abilities but often enough to give your skills and spirit a check. I competed roughly once or twice a year, and made a point of learning from every competition, win or lose (I won more than I lost but I learned more from losing).

Concept wise, consider the fundamentals of not just BJJ but of body mechanics and movement as it relates to BJJ. If you like, look into things like Rob Biernacki's conceptualization of base, posture and structure. Solidifying your own and breaking down your opponents is one way of looking at great meta concepts of what BJJ is about. Also look into some works like the book "Becoming a Supple Leopard" and YouTube physical therapists like Athlean-X help with both your body posture and movement and to help your recovery from nearly inevitable occasional injuries and for maintenance.

...all the other things I'm forgetting 😉 ....