Originally Posted by
yaganon
I just had new chains because the old ones were stretched out. Could it be that the gears are worn out as well?
Very likely.
New chains that skip under load on old cassettes are par for the course. The chains and sprockets wear together, so if your old chains were badly stretched (worn) it's likely the cassette, or at least it's most worn sprockets are also toast.
As a guideline, if the old chain is stretched 1/2% (1/16" over 12") or less the cassette should be OK. Over 1% (1/8" over 12") the cassette is likely toast. Between those numbers it could go either way.