During the installation of the retail version, did you see an option to "overwrite the existing install or install to a different location?"
We generally recommend that any trial version Office software is uninstalled first, then the system rebooted, before installing new versions, but since your install seems to have worked without any problem perhaps that wasn't critical in your case.
Does Windows 7's Programs & Features option in the Control Panel still list this Starter kit as a separate install to the new one? If so, uninstalling it from there should be OK.
But whatever you decide, best that you do it before any customization.
My Win 7 Pro 64 bit PC came with Office 2010 Starter. As best I can tell this 'Starter' edition is the home/student version that does not include Outlook.
I loaded a retail copy of Office Home and Business 2010, which appears to work OK. In a similar install on my laptop the installation of the retail copy automatically removed the pre-installed office trial version but that did not happen with Office Starter.
Do I need to remove the "Office Starter" software? If so, will that require a clean re-install of the retail Home and Business product?
I have a lot of customization to do on Outlook (installing certificates, ...) and I don't want to go down that road if I'm going to have to do everything all over again.