Elizabeth X of the United Kingdom (also known as Liz Ten) was the Queen Regnant of the United Kingdom of Great Britain and Northern Ireland when Earth was devastated by solar flares in the 29th century, but due to technological interference with her body clock, she lived (and reigned) for well over two centuries. She'd grown up on stories of the Doctor, as had her whole family, seeing him as both a hero and a strange man.
Capturing the Star Whale
Liz Ten found a star whale and enslaved it (or thought she had; in actuality it volunteered) to form the base of Starship UK. She then wiped her mind so that she would not have to deal with the consequences. Her government slowed down her body clock, keeping her effectively immortal. She thought she was fifty and had been on the throne for ten years, not knowing she always lived the same ten years, always found out the truth about Starship UK at the end of it, and always wiped her mind once more. She also placed this "voting" system throughout the ship and everyone would always choose to forget. Those who didn't were sent below, to feed the star whale. She feared that if the star whale was freed that it would then fly off, killing all who lived on the ship. She wore a mask to disguise herself from the public whilst investigating.
When the Eleventh Doctor and Amy Pond came to Starship UK, they found out the truth and told Elizabeth. Amy freed the star whale but the beast continued to carry Starship UK as it wanted to help the residents. Before he left, Liz gifted the Doctor her mask as she no longer wanted there to be in any secrets in her kingdom. (TV: The Beast Below)
The Royal Collection
In the 52nd century, she was still the Queen but showed some signs of ageing — for example, her hair greying — but by this time she was also guardian of the Royal Collection. She caught River Song in 5145 (making her at least 2150) attempting to steal a Van Gogh painting of the TARDIS exploding. After holding River at gunpoint, she saw the painting and learned whom it was meant for before letting her go. (TV: The Pandorica Opens)