First meeting with the Doctor
Carvossa was the leader of the rebels who fought against the aliens who had invaded New Houston. With help of the Doctor, they defeated the aliens. The Doctor invited her to join him and Dodo Chaplet in their travels in the TARDIS, but when she saw inside the TARDIS, she ran away in terror.
After the invasion, she became the leader of New Houston. With their supplies stretched to their limits, she went to the CIB and tampered with the records, making it appear there were more people on New Houston then there actually was. The trick fooled Earth, and they started sending more supplies.
Second encounter with the Doctor
The supply trick was still going on years later. Carvossa found out someone was tampering with records at the CIB. She went to her air car, and just about when she was going to leave, she realised she's forgotten something. As she exited the car, it exploded.
After the assassination attempt, she went and hid in the CIB. She discovered Nesca Bangate holding a gun on a man and woman. She shot Bangate fatally, and she discovered that the man was the second incarnation of the Doctor and the woman was his companion Polly Wright.
The Doctor and Polly, suspicious of Carvossa, went and freed Quilp and went to Carvossa's office, hid Quilp at Carvossa's office and went and saw Carvossa. The Doctor made Carvossa confess about tampering with the records. Quilp heard everything and had Carvossa arrested.
While walking down the street, the two robots escorting Carvossa stopped. A few seconds later, robots started to swarm out of the sewers and started smashing the shops. Quilp, Carvossa, the Doctor and Polly escaped in an air car. Carvossa only let Quilp come on the condition she told the computer that Carvossa had acted with the authority of the state.
They went to the CID, the strongest building in the city. The Doctor realised that Carvossa's tampering with the records, which the robots used, caused them to start thinking like humans.
The Doctor, after hearing the robots demands, let them into the CIB. The robots showed a video of Carvossa talking to the Doctor about the supplies as all the humans watched. Carvossa was ruined. The robots then revealed they only wanted to become citizens like the humans. Carvossa protested, but the robots held a vote. The humans voted that they could become citizens.