The most important thing to becoming a "senior" service designer is just old-school experience. You need to spend years working as a service designer and slowly but surely build the experience. It's not sexy, but that's basically it.
Sure, some things can help accelerate that path a little bit. For example:
Mentoring younger service designers helps build your leadership skills. This can be done for example, via communities like ADPlists.
Teaching service design helps strengthen your expertise.
Trying out new technics and ways of working gives you more diverse experiences.