Dora (Frontier in Space)

The President of Earth in 2540 was a female closely advised by Earth's primary military officer, General Williams.

After a series of raids of Earth cargo ships, believed to be the work of Draconia, she personally met with the Draconian Emperor's son in order to negotiate an end to hostilities. She came under pressure from both her military advisors and the political opposition to take military action against Draconia. Eventually, perhaps because of the threat of a military coup, she agreed to break off diplomatic relations. However, she refused to fire the first shot in a war.

Thanks to the Doctor, it was revealed that the raids were the actions of Ogron mercenaries and war was averted. (DW: Frontier in Space)
 * According to the novelisation, she was not the first female to hold the office. The adaptaion also sheds greater light onto her uneasy relationship with Williams.  In it, readers discover that Williams had actively campaigned against her for an "aggressive inter-stellar policy".  When she won, she appointed Williams as her military aide "to heal political wounds".  The novel also gives rise to the notion that the two were former lovers, something the episode offers only vaguely through body language.  Adapter Malcolm Hulke tells readers that the president had a silver locket around her neck and within that was a picture of a 20-year-old Lieutenant'' Williams.