This postcard is from the early 1960s.  It’s a Haynes Distributing card with the photo shot by C. H. Ruth.  Ruth and Joyce L. Haynes shot a lot of film in the Kingsport area around 1962.
Note that the visitor center is not there yet.  This is nearly 10 years after the dam was finished.

I like the lone tree sticking up on top of that hill.