Miss Dexter was a ruthless security agent working for Mr Saxon, entrusted with the task of finding the Tenth Doctor and his companions. Miss Dexter enlisted Francine Jones's help, tapping and tracing Francine's phone conversations with her daughter Martha, who was travelling with the Doctor at this time. (TV: 42)
She was at the Jones' house when Mr Saxon ordered her to arrest all of Martha Jones' family and bring them to the Valiant. After a brief struggle, Dexter managed to arrest Francine, Clive, and Tish Jones, during which she ordered her guards to open fire on Martha. (TV: The Sound of Drums)
Following the Toclafane invasion, she continued working for the Master as one of his sector chiefs in the rank of ADC, mostly from the Valiant; following his orders, she put UCF Griffin in charge of finding Martha. (PROSE: The Story of Martha)
Behind the scenes
This character's name was never revealed on screen. In both 42 and The Sound of Drums, she is credited as "Sinister Woman". However, The Story of Martha features a female character working for the Master, in charge of finding Martha Jones and with physical description matching that of Elize du Toit's character. Given that the actor herself describes her role as "Miss Dexter", it is the most plausible assumption that the name was given in the shooting script and then adopted and made public in the anthology The Story of Martha.