There would be a Republican primary if any filed to run for local offices.

I think the actual process is that the party has to request a primary -- but there is a cost involved, if I recall correctly, and so the party isn't likely to ask for a primary unless it's aware of viable candidates.

There would be a Republican Party Primary if the party requested it and presented a slate of candidates. In essence, since the local Democratic Party Primary is generally the only one held, then the winners are essentially winners by default of the August general election. However, a candidate can run as an independent but must file by the filing date for the party primaries. In counties in the state (particularly East Tennessee) with a heavy Republican influence, the Republicans are the only party holding a primary, so it works both ways. The counties fund the primaries. It doesn't cost much more to have both party primaries at the same time versus only one.

Well, unfortunately that "Yellow Dog" might be a particular female and I'm betting that even they don't want that. It would truly be a sad thing to watch this country turn into a socialist country because some people can't let go of something that happened over a hundred years ago.