I installed a newer Photoshop Elements and the old version is still installed, can I just delete the old version?
You can if you want to. One word of caution: any brushes you made, and any brush sets you added- along with things like custom palates, or shape libraries you added will have to be manually reinstalled.
If you decide to remove it, deactivate it (Help > Sign Out from the editor menu) and uninstall, not delete.
Thank you very much, if you delete the older version, the new program opens faster. But if you need to reset custom brushes, I wouldn't uninstall the older version.