A fan of any iteration of Star Trek, not just the Next Generation as elsewhere noted.
Original series Star Trek fans have had a preference for trekker, not trekkie
, going back to the early '70s and the first conventions.
At about that time, the mainstream media discovered Star Trek fandom with feature stories that usually had a condescending spin, including the term trekkie. These were along the lines of "Who are these trekkies and why do they gather by the thousands to profess their love for an old canceled TV show?"
Those features often focused on the most extreme aspects of fandom that of course looked weirdest to non-fans, and didn't delve into what it was about the show that made fans so passionate. Thus were the beginnings of the "nerdy" cliches that have come to be associated with fans. It was to avoid associations with such cliches that original Star Trek fans became opposed to trekkie and sought to get the more serious-sounding term trekker used.
"Yeah, I'm a Star Trek fan, but I'm not a trekkie, I'm a trekker. Why? Because it better reflects what being a fan is about."