What does Scrooge's clerk do?

Ebeneezer Scrooge ran a counting house. The closest thing we have these days to that business is an accounting firm. Some counting houses also served as a bank. It doesn't appear that Marley and Scrooge were bankers but they may have been lenders of money as well. Probably not friendly lenders by Scrooge's day, he was a bit stingy with his money.

Bob Cratchit was a clerk in the counting house. He'd have performed the duties of a junior accountant or bookkeeper tracking money in ledgers - not very different than the work they do today.

In those days the clerk was an apprentice to master and could advance with time to owning his own firm or becoming a partner. That's how Scrooge and Marley came to their position, as apprentices.