It’s not known who painted this artwork (given by the Friends of the Tate Gallery in 1961), which must be annoying as the Tate says that the same artist was thought to have had quite a body of work from the 1560s. It’s thought that the sitter was likely the Swedish-born Helena Snakenborg, later the Marchioness of Northampton, who was to be the chief mourner at the funeral of Queen Elizabeth I.
The painting is also a reminder of the corset and bodice arrangement that was likely seen as a fashion necessity by women of wealth and prestige at this time. The artwork is from 1569 and, two years later, she married the Marquis of Northampton who was a fair bit older than her. The gallery notes that the carnation behind her ear was likely a symbol of that betrothal.