Carson's first work in directing was in the British theatre scene and on British television. He directed an episode of the British soap operaCoronation Street. Carson sought to move to the United States in order to work in the American film scene, and prior to travelling, his agent arranged an interview for him with the producers of Star Trek: The Next Generation. However, he had never heard of Star Trek, and at his agent's suggestion, he rented some videos in order to conduct research. Once in the United States, he met with Rick Berman and David Livingstone and was hired to direct the episode "The Enemy".
The producers liked the different British style of directing and scene blocking that Carson brought to the set, as it was a style that the show hadn't previously used. He was subsequently brought back for another episode, but when he arrived for the first of eight days of preparation he was told that Whoopi Goldberg was available, and so they would like him to direct one of the scripts that she appeared in. This turned out to be "Yesterday's Enterprise", which was developed from an outline to script during the eight days of preparation prior to shooting. His other episodes of TNG included "The Next Phase" and the second part of "Redemption". He was approached by Rick Berman to direct the opening episode of Star Trek: Deep Space Nine, "Emissary". He later explained that there was some apprehension prior to the launch of the series because it was the first without Gene Roddenberry, the producer. Carson had to ensure that he stayed within the pilot's budget, and to deal with the differences between TNG and DS9 while ensuring that it appealed to the fans. His other Deep Space Nine episodes included "Dax", "Move Along Home" and "The Alternate".
Carson's final work for Star Trek was his first feature film, and the first film in which the TNG characters appeared, Star Trek Generations. During the making of the film, he fought for the death of James T. Kirk to be changed from the original scripted version as he felt that it was "ignominious". Following the poor scores the scene received at public test screenings, the ending was re-written and Carson led the re-filming at the original location. His directing work on Generations inspired cast member Jonathan Frakes to seek to direct the following Star Trek movie, Star Trek: First Contact.