Carter was the captain of the Teselecta.
Biography
Berlin
Carter and his crew first encountered the Eleventh Doctor in Berlin, 1938, shortly before the Second World War. Carter had arrived there with the intention to give Hitler hell, but was interrupted when the the Doctor's TARDIS, with the Doctor, Amy, Rory and Mels crashed into Hitler's office. When they saw Mels, who had regenerated, they recognised her as Melody Pond and stopped their pursuit of Hitler to punish her instead; knowing that she was the woman who would kill the Doctor. They were thwarted by her parents, Amy and Rory, who after being minaturised into the Teselecta, turned off the devices protecting the crew from the ship's antibodies. The crew teleported to a spaceship above the Earth, abandoning the Teselecta, which was used to show Melody that she would become River Song, a good friend of the Doctor and his companions. This helped Melody to resist her childhood programming as the Silence's assassin. The Doctor also had it reveal the Silence's purpose and extracted data from it regarding his death. (DW: Let's Kill Hitler)
Lake Silencio
The Doctor next encountered Carter and the Teselecta when he neared the end of his "farewell tour". He met with Father Gideon Vandaleur, former envoy of the Silence, soon revealing that he knew Vandaleur had been dead for six months and he was the Teselecta in disguise, deducing that the Teselecta was investigating the Silence. The Doctor made Carter do him some favours. First, he had him identify the Silence's weakest link, so he could find out why he had to die, and second, to deliver the 'Tardis blue' envelopes to Amy and Rory, River Song, Canton Everett Delaware III, and the Doctor himself when he was only 909 years old, these envelopes being invitations to his death at Lake Silencio. (DW: The Impossible Astronaut)
Carter then effectively saved the Doctor's life when he offered him an extra favour as thanks for the Doctor's unending crusade for justice. Per the Doctor's request, Carter had the Teselecta copy the Time Lord and beam him in. Allowing the Doctor control of the ship to fulfill the circumstances of his "death", Carter had the Tesselecta go to Lake Silencio on 22 April 2011, where River Song was to kill the Doctor. Following the "murder", Carter let the Doctor out of the Tesselecta. His crew and he kept this escapade quiet from the Justice Department, not only to avoid adverse consequences, but to keep the Silence from constantly trying to kill the Doctor. (DW: The Wedding of River Song)
Personality
Carter was a well meaning man who was extremely devoted to justice. He respected the Doctor, seeing him as a master of law and order and offered to help him before the Doctor headed to Lake Silencio to die. Carter saved the Doctor's life by allowing him to use the Tesselecta to fake his death. However, despite his good intentions, Carter was also rather sadistic and often tortured people if he felt they deserved it, showing no concern about the agonising pain he put them through. Because of this, the Doctor respected the Captain of the Tesselecta less than Carter respected him. (DW: Let's Kill Hitler The Wedding of River Song)