To be promoted in my school as an NTT, one needs external letters of recommendation. The requirements are similar to the tenure promotion recommenders (basically, the recommenders cannot be your friends/colleagues, etc.). The recommenders are supposed to comment both on my research and teaching.
Well, you ask (sufficiently senior) people in your field to write you a recommendation letter. This is not common, but also not extremely rare - I have personally written around five such letters in about as many years. Of course not everybody you ask will say yes, but it's also not an outrageous request. That you don't know them personally isn't so uncommon either, some places (most notably the US Department of Homeland Security) explicitly ask for recommenders that you have never even spoken to.
Of course, these letters are different from the kind of letters you would get as an aspiring PhD student - everybody understands that if you ask for a letter from somebody with no conflict of interest you are not getting an evaluation of you as a person, but rather a judgement of how impactful and visible your work is in your field. That said, it is similar in the sense that if you struggle to find people agreeing to write you a letter, one problem may be that your work is indeed not very visible and all the people you ask decline rather than writing you a poor letter.