If you're trying to do scrum properly, you shouldn't be consistently finishing work early. That implies you're overestimating stories. When you do finish a bit

If you're trying to do scrum properly, you shouldn't be consistently finishing work early. That implies you're overestimating stories. When you do finish a bit early I've not normally found it a problem to find some small bits of tech debt, research, or admin work to fit in before the end of the sprint. Starting work on stuff from the next sprint is not ideal because it'll throw your estimates off for the next sprint, plus you don't actually know for sure what is going into the next sprint.