It's common for new chains to skip under load when combined with used cassettes. At only 500 miles I'd expect your cassette to be OK, but you never know. The easiest way to check is to try another wheel or cassette. If the chain runs OK with that, you know that you need to replace the cassette.

It's almost impossible to determine the wear age of a cassette by eye, but if you still have your old chain measure that for wear using a ruler. Since it's off the bike hang it on a nail and measure 4' using a steel rule, and measuring from the first link to the same place on a link 48" ( 96 links) out. I'd suspect that your cassette is toast if that distance is 48-1/2 inches or more. If it's nearer to 48-1/4 or less, your cassette should be fine, and you'll need to look elsewhere for the cause of your skipping.

BTW- if it turns out your chain was stretched beyond the limit in only 500 miles, consider chainging your chain lube (I have to say that) ans/or your chain maintenance practices. You should be able to do much better than that, and you prevent cassette wear by reducing chain wear and replacing the chain at 1/2% (1/16" over 12") stretch.