At first glance, this seems to be a classic "new chain skips on old sprockets" issue. This is extremely common and very likely if the prior chain were very worn. Stretched chains create a slightly hooked wear pattern on sprockets which cause new chains skip. If it's very minor (doesn't skip all the time) it'll self resolve as the chain wears away the offending areas, but serious or chronic skipping will wear you out before it wears itself out.

As I said, that a quick diagnosis based on the obvious clues, but doesn't rule out things like a trim adjustment which is an easy fix. Do the regular checks, and see if you can live with i a while, but is sounds like you need a new cassette.