If you are looking to do a BM degree, you will have to apply to the school of music and the university as a whole academically, and you need to get into both to get in. With the school of music, it is going to be your audition and having a teacher want you in their studio (the academics won’t matter with the music school portion of the admit, the academics count with the university admission).
As far as teachers “holding” spots, I think you need to understand how music schools and studios operate. To get admitted to the music school, you need to audition for a panel, and then if that works out, a teacher has to agree to teach you. Most of the music schools I am aware of, when you apply you specify the teachers you want to study with (usually like #1, #2, #3), then after you audition the teachers indicate yes or no, and a match is made that way (some schools, like IU Jacobs, you get admitted then work to find a teacher).
in terms of spots, usually teachers have a certain number of kids they teach each year, some of the ‘famous’ teachers like an Itzak Perlman or Jimmy Lin only teach a small handful of students, so each year they may take 1 new student, other teachers may have anywhere from 1 or 2 to half dozen, depends on how many kids graduate from their studio or leave. It is very different than sports, the open slots in the department on an instrument depend on how many open slots the teachers on that instrument have, there is no magic number, and it isn’t like they take slots away from the violin department to give them to the cello (least as far as I know). The only thing I am aware of that might match what you are asking is a teacher who technically doesn’t have an open slot that year, if they see a student they really want to teach, might fight to get an additional slot, and I have heard rumors that in some programs that teachers “horse trade” , that because the place admits relatively few students, teachers will bargain with the other teachers about getting someone in or they will horse trade to get a student in who may be on the margins of getting in they like, bargaining to allow another teacher to get a student they want in who may be marginal, but I am kind of dubious about that, given the level of playing at that school in the particular department.
For the most part, it is relatively straightforward, though, the teacher has x slots, and decides among the undergrad and grad applicant the people who fill those slots, and those slots are determined by the teacher’s capacity - current students returning. The idea of holding spots implies that somehow the kid they want wouldn’t pass the audition process (for if they can pass the audition, then the teacher simply would say yes to teaching the kid, the kid would select him, and voila), and a teacher to be honest would have little reason to admit a kid who can’t pass the audition, it would look pretty bad to have a student like that, so why would a teacher bother because they decide who they teach, not the school.