The Diagnostic Server will automatically upgrade the old Spotlight Statistic Repository when it is first detects it. So just link the new Diagnostic Server to the old Spotlight Statistic Repository and the Diagnostic Server will do the rest.
Keep in mind that you need to consider the version of the old Spotlight Statistic Repository. If too far back, the Diagnostic Server may not be able to upgrade it. The best thing to do is to review the "Upgrade and compatibility" section of the Release Notes. While this section talks about the Spotlight version that you need to be on before you upgrade, the principle applies to upgrading the Spotlight Statistic Repository as well.
The Release Notes can be downloaded from the Quest Support Portal.