Originally Posted by FBinNY

Sprockets don't age in years, they age in miles. You sprocket could be 50 years old and in mint condition, or 1 year old and ridden until it was worn out.

That said, a chain replaced because it was stretched or skipping on the cassette, probably means that the cassette also needs replacing, but it's not certain. Yhe only way to know for sure is to replace the hain and test ride.