This is an antique portrait oil on canvas half length portrait painting of a seated woman in oil on canvas. There is a tag on the frame that identifies the sitter as Elizabeth, Duchess of Queensbury (1743 - 1827) and the artist as Catherine Read (1723 - 1778). In addition, there is a past auction sale tag showing that this had once been sold through Christie's Auction House at some time in the 20th century. Identifying tags on frames are to be considered with a grain of salt especially when the painting itself is unsigned. In this case, there is a known portrait of Lady Elizabeth Montagu, Duchess of Buccleuch and Queensberry from 1767, the year of her marriage, by the famed Thomas Gainsborough.

(Here is a link for you to that image: https://commons.wikimedia.org/wiki/File:Lady_Elizabeth_Montagu,_Duchess_of_Buccleuch_and_Queensberry.jpg )

Comparing the known image to yours does show a physical match to the subject in your painting. However, in your painting, if Catherine Read were to have painted this portrait at near the end of her life in 1778, this would mean Elizabeth, the subject would have been around 35 years old at the time. In this portrait, Lady Elizabeth appears to be older than 35 years. In addition, comparing this work to known works by Catherine Read, the style of this work is markedly different than the painterly stroke and rendering style of Read. In conclusion, this work is a late 18th century portrait of Lady Elizabeth Montagu, Duchess of Buccleuch and Queensberry (1743 - 1827) however it was most probably not by the hand of the artist Catherine Read. Without a signature, the author of the painting is unknown. The heirs of Lady Montagu may have receipts filed from her lifetime identifying the artist, however making such contact would be an endeavour in itself. The estimate is based on actual recent past recorded auction sales of comparables. Retail 'asking prices' can be higher and vary.