Is it ethical to refuse enrollment of a previously dishonest student if you are the sole instructor for a required course? I am currently teaching an upper level course, and have caught a student plagiarizing this semester.  This course is required by our department for a degree.  I have strict policy on my syllabus that states plagiarism will result in failing the course, a judicial review incident report, and refusing to accept them as part of future cohorts.  Next semester however, I am the only instructor for this course, and possibly again for the following Spring.

I've been pushing my department to add more instructors, as I don't like being in a position where students who are incompatible with my teaching style are forced to take me over and over again, but they are having a difficult time finding someone.

Personally I do not want the student in my class again.  They have been nothing but trouble the entire semester.  From my interactions with the student, they don't have the required prerequisites at anywhere near a passable level, they are disruptive during class, and I had an inkling that they were trying to cheat off their neighbor during examinations.  (I had ensured that every other test was different so I didn't pursue this)

Should I just grit my teeth and waive this policy since they have no other path to graduation?
It's not up to you

It's reasonable for an instructor and syllabus to specify what happens in that course in certain circumstances. However, going beyond your particular course (including future semesters of it), any further academic punishments for plagiarism or cheating, including being restricted from taking or retaking certain courses, are up to the wider department, faculty, study program, or however your institution organizes things. There should be a universal (not made by and for a single course and instructor) policy on what are the wider consequences for certain acts of plagiarism. Perhaps that policy prescribes that being forbidden to retake that course (or some time limit) is an appropriate punishment, in which case your actions are valid. But if it does not prescribe that students will be prevented from taking future courses, then it's not up to the course syllabus or the instructor to unilaterally decide whether the student is eligible or not.

Note that I'm not saying that you should waive the policy just because it disrupts the path to graduation - there certainly can be academic dishonesty policies that may prevent students from graduating in case of plagiarism. But the question does not mention any specific wider policies, and if it eventually does come to a ad-hoc decision regarding a particular student, that still would not be your decision to make, this should be escalated to your superiors.