When you say clench, do you mean clench the muscles (i.e. as if biting down), or do you mean jutting your jaw forward?

There is a well known phenomenon among people with (at least some types of) tinnitus that moving the jaw forward increases the sound, but that this also makes the tinnitus go away for a bit. The way my ENT explained it, it has to do with how your brain calibrates sound. Pushing the jaw forward makes the sound louder, which also causes your brain to adjust your hearing to be less sensitive. Or something like this.

With some types of tinnitus, there is a specific connection to the temporomandibular joint. My understanding is that the causes tinnitus are poorly understood, however. There are many hypotheses, but little solid evidence.