A few months ago I shared a list of published opinions on how to avoid undertones on the clarinet.
Many of the ideas shared by the distinguished authors seemed like just descriptions of good basic clarinet technique (“ensure correct, stable embouchure formation,” “establish breath support/air pressure before releasing tongue”). I agree that the most important way to improve undertones is to have a solid baseline tone production technique. If you can play with a beautiful, characteristic tone, mostly in tune, with good response, then your undertones are probably mostly gone already.
I do have one small tip that I find helps a great deal with clearing up any remaining undertones, that wasn’t mentioned by any of the sources I consulted. My readers know I frequently discuss the importance of keeping voicing very stable, but as I have indicated previously that’s only one side of a multifaceted issue.
I have good success with lowering my voicing just a little bit in the upper clarion register. (I tell my students to think of warming the air by just a degree or two.) This seems to stabilize and clarify those notes.
As always, expect any change in voicing to have multiple consequences, for tone, pitch, and response. In the case of clarinet upper-clarion notes, I find a very slight lowering of my voicing to have only minimal and acceptable effects.
If anyone is aware of others teaching this technique, I would be curious to hear about it.