Lady Arabella was born in 1575 to Charles Stuart (1555-1576), younger brother of Lord Darnley, and to the very wealthy Elizabeth Cavendish (1549-1582). As her parents died so young she was brought up by her maternal grandmother, Elizabeth Hardwick (1520-1608), the wealthiest person in England after Queen Elizabeth (I think it was that way, but I might be wrong). She was in line to the throne after James VI of Scotland, for whom she had been seen as a wife for some time. She was intelligent and attractive although I think she wasn't particularly beautiful.
In 1603 her cousin became King of England. James, who never trusted anyone, thought she was a potential rebel and treated her with coldness. When she married William Seymour (12 years her junior!), who also had a claim to the throne, in 1610, James thought there was being some type of plot against him and he threw the couple into the Tower of London. William was released soon after, but Arabella died there in 1615, aged 40. Apparently she died of natural causes, but many think a convenient poison was given to her. She died without issue, so she was no problem any more for James!