Thanks again Stan. One of the Maltsters mentioned in the 1822 Directory was a Smith. And by looking at John Smith's Brewery on Wiki, I find that Stephen Hartley started brewing in Tadcaster in 1758, and his grand-daughter, Jane, mortgaged the brewery to David Backhouse and John Hartley (I assume her brother, born in 1799) in 1845. It was Jane's baptism which gave me the occupation, and that also mentions that her grandfather was Stephen. Stephen had married Mary Cowburn, the daughter of James Cowburn of Tadcaster, a Maltster. Jane died in 1852 and John Smith acquired the business.
I do like it, when it all comes together

Added: I did get it a bit wrong - Jane who sold the business is, I now think, the widow of William Hartley (third wife). My original assumption being Jane, daughter of William Hartley and Mary Archbell (second wife).