She was Queen consort of Spain and is also known as Elisabeth of France, eldest daughter of Henri IV and Marie de' Medici. Her daughter Maria Teresa married Louis XIV. From Artnet:
A recent conservation undertaken by the Prado Museum, which holds the work, has restored the painting’s original depth and colors, with the lateral additions newly blended into the main canvas. This effort is part of a project to restore Velázquez’s equestrian works.
“The queen has recovered the regal bearing and the serene and natural beauty with which she was portrayed,” María Álvarez Garcillán, of the Prado’s conservation department, said in a statement. “With unique mastery, the horse once again shows off its qualities in a display of naturalism that only a genius like Velázquez is capable of recreating.”
Velázquez’s Queen Elisabeth of France, on Horseback was created as one of a series of portraits meant to adorn the Salón de Reinos, a wing of the Buen Retiro Palace in Madrid. The great hall hosted soirees and spectacles, as well as paintings celebrating the monarchy. Isabel’s portrait was intended to hang with that of her husband Philip IV and their son Prince Balthasar Carlos—all of them depicted on horseback.
In ways, Isabel’s and Philip’s equestrian portraits both complement and contrast with each other. Velázquez’s opted to place the queen on a white horse, echoing the stripe on the king’s rearing stallion. Where Philip is portrayed with a forward gaze, Isabel directs her eyes to the viewer, appearing composed atop her horse’s blanket and lavish gown bearing her anagram, which was not painted by Velázquez himself. (Read more.)