a freelance teacher

maybe


sup'ply teacher (BrE)
employed to do the work of another teacher who is away because of illness, etc.

There IS no definition for "Honorarlehrer" in the LEO dictionary. The LEO definition of "Honorar" (a fee for a service, as with a doctor or dentist) suggests that the English meaning of "Honorarlehrer" is "tutor" -- that is, a teacher who gets paid for each teaching session -- typical with private music lessons, or for students who need special instruction and whose parents can afford it!

If this means a teacher who is not the usual one (that is, if the usual one is sick, etc.), then the US English expression is "substitute teacher." But the correct German for this according to LEO is "Aushilfslehrer".

Tutor hits it perfectly - thank you so much for your help! I didn't understand the German word.

Just a clarification -- "tutor" is used for individual instruction in academic subjects, as a supplement to regular instruction at a school, or when the student does not attend school due to an illness, disability or between school terms, or when the family is so wealthy that the student receives private instruction and does not attend a school. But in the case of fee-for-service, one-on-one instruction in music, the word "teacher" is used, as in "violin teacher".