It depicts the Scottish politician and lawyer William Murray, 1st Earl of Mansfield who was serving as Lord Chief Justice at the time.
The year Copley painted him he made a major ruling in the case of the Zong slave-trading ship.
Copley was an American artist who emigrated to Britain in 1774 and enjoyed success with his history paintings, although he continued to produce portraits.
A few years earlier Copley had depicted Mansfield as one of many figures in his large work The Death of Lord Chatham.
In the background is a bust of the writer Alexander Pope, who Mansfield had been friends with in his youth and who mentioned him in his Imitation of Horace's Epistle.