Photo credit: Royal College of Physicians, London
Was this perhaps painted by Robert Home?
According to the painting description, it is doubted that Scottish-born Alexander Russell (1715–1768) is the sitter for this portrait, as the features here are inconsistent with the well-known engraving after Nathaniel Dance by Thomas Trotter.
The portrait is thought more likely to be a man from a later generation of the Russell family.
Based on the sitter's apparent age, dress and hair, he is not someone born in 1715 but later, c. 1750.
If this is by Home, it seems above his average level.
I have to agree with Jacinto, if this is by Home it's the best portrait he ever painted. Besides his own. https://www.npg.org.uk/collections/search/portrait/mw03219/Robert-Home?LinkID=mp02250&role=sit&rNo=0 and there are no similarities. Too much Normal Guy Character exuding from the painting to be Reynolds. Romney wasn't this good not with Men anyway. Not painterly enough for Gainsborough. Should I point out it feels American. Just a Guy in his Best Coat and Shirt with a pleased look on his face.
It Could be Sir Henry Raeburn. It's of that quality. But even Raeburn's regular guy portraits have a feel about them that's lacking here.
This is an engraving that purports to be your suggested sitter. https://upload.wikimedia.org/wikipedia/commons/c/c4/Portrait_of_Alexander_Russell_by_T._Trotter_Wellcome_L0011163.jpg
Input from a costume expert to narrow down the date would be of use.
Whilst waiting for a Costume Expert I Looked around some more. Yeah I Know I don't have a life. Anyway,lol. Take a look at his self portraits as well as some of his portraits. Notice the same green in the background and the faces that look present and not about to go off and conquer the world. He appears to be mostly forgotten. He Trained in London, very talented, and then moved back to the Midlands. https://artuk.org/discover/artworks/search/actor:wright-of-derby-joseph-17341797/page/7 and the winner is Joseph Wright. Maybe.