If you get a new computer, do ya migrate from the computer that is currently used, or do ya use the trial/other software on the new machine.. If it's that later, does the license renewal get prolonged?
You can just download the software from your online account at the McAfee web site... if you have this. When you get a new computer thee's usually antivirus software installed plus some other security software. Good thing is to uninstall it first before installing the new McAfee software. If you get McAfee's trial software with the new computer then it's also recommended to uninstall the software first. You can also use the removal tool. Check this document: How to uninstall or reinstall supported McAfee consumer products using the McAfee Consumer Products ...
If you wish to use the same products on other computers you must purchase extra licenses (not products but mere licenses) If your product has extra licenses on it already you may install a copy on the other computer provided like Jubo said..remove anyother Security application (including any trial of McAfee)
See if this Documents helps you in setting up the new computer for a proper installation