There is plenty of good water on Greenbriar, like many smoky streams the farther you walk the better it gets, espeicially if you enjoy solitude while your fishing. It also depends on the time of year, as you generally need to head farther upstream during the summer months, whereas the lower portions can be good in spring. If you you want to get into broookies a little sweat will generally improve your chances as they become more dominant as you head upstream. A good trail map can be helpful if you wish to explore the headwaters.
Good luck, and have fun!