I try to fish the Holston several times in April-June for the caddis hatch. I only hook up once every 10 bites or so but dry fly fishing is just so fun it is still worth it.
The water above Nance's Ferry seems to fish well in the winter and there are several shoals/riffles that you can wade/hike to upriver from the parking lot. By about June it seems to get a mix of trout and bass as the water warms up. Use a streamer and you will end up catching some of both. Later in the summer it is a good spot for smallmouth and carp fishing. Others on this board have a lot more experience on the Holston than I do but I have generally only caught stockers down river while there are some (large) holdovers further up river.