The woman in Zoffany's portrait is Mary Oswald (died 1788), a wealthy Scot.
Mary grew up in Jamaica where her father, Alexander Ramsay, built a successful business trading in the former British colony. On his death, Mary inherited her father's substantial estate and business. She returned to Britain with her mother, leaving the business in the hands of trustees.
In 1750, Mary married Richard Oswald, a Scottish merchant she had met in Jamaica. Oswald had started his career as a merchant importing tobacco, sugar and wine for a company managed by his cousins. From this he built his own trading empire, which included providing army supplies, shipping and slaving. The couple enjoyed a luxurious lifestyle with a stately home in Ayrshire and an impressive art collection.
The costume and hairstyle suggest a date in the first half of the 1760s. Zoffany more often portrayed female sitters in conversation pieces rather than full-size portraits.