My question relates to the excellent answer given to this question a couple of years ago "Crossed vs nested random effects: how do they differ and how are they specified correctly in lme4?" The answer used the examples of classes within schools, where each of 3 schools had 3 classes that made up a nested structure of classes within schools. Here classes 1 to 3 in each school had no particular relationship and no expectation that class 1 in a school would be more like class 1 in the other schools (a random factor). My question is how would you treat a situation where classes 1, 2 and 3 did have some relationship across schools - for example: class 1 = a novice teacher; class 2 = a moderately experienced teacher; class 3 = a very experienced teacher? Here you might expect teacher experience to be important, but that effect occurs within the context of each specific school.
As eluded to in the comments, the situation where there is a systematic effect of the teacher, in this case the experience of the teacher, then one approach would be to include the number of years experience of the teacher as a fixed effect. It would be advisable to still include the class as a random effect, as there will likely be other, unmeasured, reasons for variation at the class level.