I am a middle school director that teaches high school lessons during the school day. I would never consider taking money from my students. The district already pays me to teach there is no reason for them to pay me.
If lessons were after school, you get a stipend that covers outside of school hour activities, I would just chalk it up to that.
I could not teach lessons to my own students for pay, whether the district allowed it or not (within or outside the school day at any location--school or home). I went a step further and wouldn't accept pay from any student attending a school in my school district...their parents pay taxes for my salary as well. As for students outside my district--perhaps, but my available time was very limited and any lessons would be taught outside the school day. In the present time it would not be at my residence, and wherever else, definitely with the parent or another trusted adult present and in sight.
If you're talking about a director being paid to teach their own student's lessons, then NO! The school is already paying you to teach your own students. It's just part of the job.
Beagle below is correct, you should check your board documents for any specific rules that apply. But you asked for thoughts...
We have a couple of directors in our district who teach lessons. One in particular teaches their own students, in the band hall after school or on weekends, for pay. I think it's ethically dubious at best. When I brought it up to our DFA I was essentially told to look the other way.
I think there are arguments to be made that you could teach kids from another campus, or even your own kids if it was over the summer. We have a director who teaches from home all summer, and I have less of a problem with that. Having kids over to my house is a personal boundary that I don't cross. I intentionally live in a different town from where I teach for many reasons.
I may be in the minority, but I just think it's a bad look. Too many ways for accusations to be made. I help my own kids in my office during lunch or after school, and I don't charge. I don't invite kids to my house for lessons, I don't go to theirs, and I don't use the school-owned facilities for personal gain.
I do teach all summer at the local music store. Brass lessons aren't popular but I also teach piano. Every once in a while one of my students will sign up. We have a quick discussion about boundaries and expectations at the first lesson, and it's never been a problem. Having the layer in between makes it cleaner. The kids pay the store, the store pays me. Staff development week is my last week of lessons, so I'm never teaching a kid who is currently in my class.
Make 100% certain you are following ALL board policies. Every school board is different here, so you need to consult your OWN board policy documents, not accept someone else's answer from here on TYB.
In some districts, teaching lessons is forbidden, end of discussion. In some, you can teach but not on campus. Some allow on-campus lessons but you're required to pay for the space. Rationale is that you can't be there in a professional capacity (opening the facility) AND profiting off of it a la a subcontractor. Some have no restrictions at all, except that lessons cannot occur during the school day.
You also spend a lot more time with kids you already spend a lot of time with. I've seen it result in a lot of ended careers, if you know what I mean.
If you can, hire a private staff from the community. If your town isn't close enough to a college or doesn't have a local community band, ask to see if you can use your MS director to tutor your HS kids, and vice-versa. Or if your elementary teacher is willing to teach lessons.