The listed title for this is Hon. Emma Cunliffe, later Emma Cunliffe-Offley. Her birth date is not listed, but her younger brother was born in 1772 and Emma looks like a twenty or so year old. According to her article in thepeerage, she married Foster Cunliffe in 1809 so this portrait was done in 1809 or later. According to the article in theperage about her husband Foster, "In 1829 his name was legally changed to Foster Cunliffe-Offley when he assumed the name and arms of Offley."
From fineartamerica.com/featured/honorable-emma-cunliffe-later-emma-cunliffe-offley-thomas-lawrence.
Bridgeman Art dates this to between 1809 and 1830. Between 1809 and 1814, maybe earlier, is probably more appropriate - this is a simple classically-inspired dress. This is a bit of SWAG (Scientific Wild-A__ed Guessing), but I estimate this dates from about 1800.
Keywords: Lawrence, Emma Crewe, Emma Cunliffe, Emma Cunliffe-Offley, British, curly coiffure, cap, strap, square décolletage, quarter length tight sleeves, waist band, Empire waistline, close skirt, wrap