Solve the problems you want to have
A common piece of professional advice is to dress for the job you want, not the job you have. The idea is to display your wishes without over stepping your role; to give confidence that you are ready for the part. If you dress for the job you have, your managers may never see you as anything else: you need to help them by telling them a story, the story of you being in that other role.
Similarly, it's interesting to think about solutions to the problems you want to have. It will affect the way you talk, what you see as a risk, what you see as a benefit. The problems you identify will be different and the solutions you promote will highlight that. Eventually you will become the go to person for that area and it will make it easier for you to request a move to that position.
Of course this works for promotions but it also works if you want to work in a different team, on a different feature, or on a different project.
Don't drop your current responsibilities, just add new ones related to what you want to do next. Reach for it, because no one is going to hand it to you if you don't show your interest and your competence.