There will never be any more of these due to CBS licensing requirements, but I think these 11 episodes are the best Star Trek fan series that was ever made.
Star Trek Continues is an American fan-created web series set in the Star Trek universe. Produced by the non-profit charity Trek Continues, Inc. and Dracogen, and initially co-produced by Far from Home LLC and Farragut Films, the series consists of eleven episodes released between 2013 and 2017. The series is an unofficial direct continuation of Star Trek: The Original Series, and emulates its visual and storytelling features to achieve the same look and feel. Those who made the show have said in interviews that the intent was to finish the original five year mission of the show, and this is borne out in the plot lines of the final two episodes
Star Trek and all related marks, logos and characters are solely owned by CBS Studios Inc. This fan production is not endorsed by, sponsored by, nor affiliated with CBS, Paramount Pictures, or any other Star Trek franchise, and is a non-commercial fan-made film series intended for recreational use. No commercial exhibition or distribution is permitted. No alleged independent rights will be asserted against CBS or Paramount Pictures.