In summary

1. Project management

2. Internal politics, lobbying and negotation

3. Visual communication

4. Writing

5. Bonus: understanding technology

In details

The first skill that I had to learn the hard way but that I think is valuable to any service designer is project management. Once you have this skillset, you can not only be someone who produces but also someone who organises bigger projects.

The second skillset I'd recommend to learn about includes: internal politics, lobbying and negotiation. These are the skills that you'll need in a big organization to convince, get buy-in and make projects happen.
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I've also noticed that there were skills I had before coming to Service Design that proved to be extremely useful:

1. Visual communication: being able to quickly make a good-looking presentation or prototype made me so much faster than other colleagues.

2. Writing: a good chunk of the service design work I do is summarising either research elements, decisions made in a workshop or an idea. Not being afraid of writing helps a lot.

Finally, a bonus skill if you already have all of this is to understand how technology works. You don't have to be a coder per se, but at least understand what's possible and what isn't. Having built something with no code tools like bubble or Glide, for example, is a good way to get into that mode.

My answer in video

Parts of this answer come from a video I shot for Horváth Zsóka a Service Designer practitioner from Hungary.

Going further

This video sparked an interesting conversation when I shared it on Linkedin.