On the second disc of Cheers The Complete First Season on DVD I found the episode Romans And Accountants and in the episode it is revealed that the character Norm worked for an accounting firm. But at the end of the episode Norm got fired because he got into a fight with his boss at the Greek themed party at Cheers
Did Norm get a new job as the seasons of Cheers went on?
Bestie

Yes, Norm worked for an accounting firm on Cheers in the first season. He later had another office job (as seen in an episode where the Cheers gang visit him @ work).

Later, he had a job as a house-painter, which was sporadic.

Towards the end of the series, Norm seemed to be completely unemployed. He seemed to get to Cheers when the bar opened every day & stayed there until beyond closing time - LOL.

In S10/S11?! he did have a brief job as a beer taster, but that didn't last long either - ha ha.