Why not give or receive a small gift around holiday time? Usually it is simply a small token of appreciation for the instructor, or for a continuing student.
I used to give a small gift to each student, but then I realized that many parents took this as a need to reciprocate with a gift to me, but it shouldn't be that way.
Now I give each student a choice of one sheet music piece, and usually I will also give them a holiday card. If parents reciprocate that is fine, if they don't, that is fine too.
I tell my younger students that the gifts that I like the most are the ones that he or she made; e.g., a drawing of a piano, or a self-portrait of themselves at the piano. I save these, and they are fun to look back upon as the student grows older.