Most
Star Trek fan productions are pretty horrid, but an exception is
Star Trek Continues. It was an attempt to depict the
Enterprise's final year of its 5-year mission before it returned to Earth prior to the events of
Star Trek: The Motion Picture. Basically a fourth season of the original three-season series. The acting is pretty good, the duplication of original sets, costumes, etc. is spot-on. Some episodes do have the PC preachiness-morality play elements of the original show, but I found it enjoyable for the most part and about the closest thing to an actual
Star Trek episode aired by NBC from 1966-69.
https://www.youtube.com/user/StarTrekContinues