I upgraded the Search Application from SharePoint 2010 to SharePoint 2013, implemented People Search Core Results webpart, clicked on a person returned in People Search Core Results and get forwarded to the SharePoint 2010 farm. How do I return results from the SharePoint 2013 farm?
After upgrading from SharePoint 2010 to 2013, need to verify the content source crawl path like below :
Note : Here My site host URL should be from SharePoint 2013 URL.
And also, verify people search result page from site search setting, check any custom page was created which points to SharePoint 2010... or you can create a new search result page for people search from SharePoint 2013.
For details configuration of people search in SharePoint 2013, please read the below MSDN documentation :