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.