The fishing should be good. I live farther east near the South Holston and Watauga tailwaters and April is fine for these rivers. Info on the Clinch can be had from
http://www.creelflyfishing.com/, a Knoxville fly shop. One factor that you may not be familiar with will be generation schedules. Clinch is the tailwater below Norris dam and fishing conditions will vary because of water release from the dam for generation. When it's off wading will be possible; when it's on the only way to fish it will be from a drift boat.The Tennessee Valley Authority operates Norris dam and the generation schedules are posted on their website and available by phone. The Creel will help you get the information you need to make plans. You won't be too far from the Smokies and some great fishing in mountain streams so it might pay to bring along a shorter rod in case the schedule keeps you out of the Clinch.