It likely depends on what part of the Clinch you are fishing.
If you are in the Clinch that flows into Norris where they don't routinely stock trout, you wouldn't need one.
If you are in the Clinch below the dam where trout are stocked, I would suspect a high likelihood of a citation if you don't have the trout license. If you are fishing some huge striper lure, you might get by with it. But, with any type of lure that routinely catches trout, I suspect the officer will cite and let the courts decide.
If that is the section you are inquiring about, it probably isn't worth the hassle and potential trip to court.