I think that escalate is probably the most common one-word term for this action, at least in the United States.

Merriam-Webster Online continues to offer the same definitions of escalate that it has used since the verb (a back formation from escalator) debuted in the Eighth Collegiate Dictionary (1973):

intransitive verb: to increase in extent, volume, number, amount, intensity, or scope (a little war threatens to escalate into a huge ugly one — Arnold Abrams)

transitive verb: EXPAND 2 [that is, "to increase the extent, number, volume, or scope of : ENLARGE"]

Neither of these definitions fits the poster's case. However, as Autoresponder hints in a comment above, escalate has also been used since at least 1969 in the specific sense of "take [an issue] to a higher-level authority on appeal," which appears to be precisely the sense that the poster has in mind. Why Merriam-Webster hasn't acknowledged this particular meaning of escalate after not less than 45 years of consistent usage in published writing is a mystery to me.

From Hearings, Reports and Prints of the Senate Committee on Labor and Public Welfare (1969) [snippet]:

In at least four of the above instances, the Regional Director upon disagreement with the Regional Legal Services Director may institute appeal procedures which escalate the issue in dispute to the National Director of the Legal Services ...

From Frederick Mosher & John Harr, Program Budgeting Visits Foreign Affairs (1969) [combined snippets]:

He would depend on the arts of persuasion, having little power to force the issue. His only recourse if rebuffed would be to escalate the issue up the chain of command in State. Short of the Secretary (and Under Secretary), no one in State had real authority to force an issue with another agency. Naturally, few desk officers would take this route except in the rare case in which they were dealing with a vital policy matter ...

From Riots, Civil and Criminal Disorders: Hearings Before the Senate Committee on Government Operations (1969) [snippet]:

Senator JAVITS. It occurs to me and my people, Dr. Abram, you may find the right course because I am interested in the procedure. I, too, will be against Federal law creating new criteria, but I do think there is something to be said for a remedy in the Federal courts which does escalate the issue to a higher judicial level.

From Proceedings of the Federal Management Improvement Conference (September 21 and 22, 1970) [combined snippets]:

When an issue arises, employee representatives are inclined to engage in a "shopping around" tactic by approaching various management officials regarding the issue. They "shop" until either they get the answer they want or have so many different "official" views that they can escalate the issue to higher authority. There is nothing so embarrassing to management or so useful to a labor organization than to get two or three "official" and conflicting positions on an issue.

These examples strongly suggest that this particularly sense of escalate arose in U.S. federal government jargon; but it has since spread to business (and elsewhere) while remaining common in government work as well. From Stewart Liff, Managing Your Government Career: Success Strategies That Work (2009):

If you are not satisfied [with a supervisor's response to a complaint], you then have two options: Either drop the issue or pursue it further. If you decide to escalate the issue, give your supervisor the courtesy of knowing that you plan to go over her head. While she may not like it, at least she will not be caught off guard. Pursue the complaint as professionally and unemotionally as you can; simply state the facts, indicate why you feel aggrieved, and identify the remedy you are seeking.

And from Michael Bender, A Manager's Guide to Project Management: Learn How to Apply Best Practices (2009):

The purpose of the control limits is to signal when the project is in trouble. Classically, when the cost variance percentage or schedule variance percentage crosses the inner control limit, the project management team must take action. If either variance percentage crosses the outer control limit, the project manager must escalate the issue to senior management. The location of the control limits varies among organizations and project categories.

In none of the examples above does escalate refer to increasing the magnitude of a conflict; rather, it refers to appealing a lower-level decision about a conflict to a higher-level authority. In that respect, the connection to the noun escalator seems quite rational. I should perhaps also note that, although all of the examples reproduced here are from Google Books search results for "escalate the issue," Google Books finds similar (though not as early) results for "escalate the matter," and "escalate the dispute."

If you do decide to use escalate in the context of an appeal to a higher hierarchical level in a dispute with a teacher, you'll be using the word in a now-common way. (Note that the verb escalate in any sense has been around only since 1944, meaning that the "raise to a higher level in an organization" sense appeared within 25 years of the word's first sighting, and has enjoyed increasingly widespread use during the 45 years since 1969.) Specifically, you might frame the relevant sentence as follows:

If you decide to escalate the matter to someone who is above the teacher in the school hierarchy, always tell the teacher your intention and that you're unsatisfied with the outcome of the situation.