Lady Caroline Howard, daughter of Frederick, the fifth Earl of Carlisle, and Margaret Caroline Howard, and niece of Lady Delmé, was portrayed by Reynolds at the age of seven.
Reynolds deliberately imposed on his compositions certain formal artistic qualities that would give them the solidity and nobility of Greek, Roman, and Renaissance art. He also liked to suggest associations in his portraits that elevate them to some level beyond the merely descriptive. Roses are symbolically related to Venus and the Three Graces, and Reynolds may well have intended to allude to their attributes, Chastity, Beauty, and Love, as ideals to which Lady Caroline should aspire.
Lady Caroline's father affectionately described his daughter as a determined, strong-minded child whose need for discipline he met fairly but reluctantly. He wrote that she was "always a great favorite," suggesting that her spirited personality made her faults tolerable. Reynolds captured some of Lady Caroline's complexity in the serious, intent expression of her attractive face, her averted gaze, and the tension implied in her closed left hand.
More information on this painting can be found in the Gallery publication British Paintings of the Sixteenth through Nineteenth Centuries, which is available as a free PDF https://www.nga.gov/content/dam/ngaweb/research/publications/pdfs/british-paintings-16th-19th-centuries.pdf