I have not lived in Tennessee for years and have been claiming the non-resident exemption. This year I [provided a little advice or Tennessee law/ made a short appearance in court/ filed a legal document and the case closed days later]. Can I still claim the non-resident exemption for this compliance year?

No, if you practiced Tennessee law, even briefly, you cannot claim the exemption for the year. Remember that providing counsel and advice counts as the practice of law.