To upgrade a Windows 7 lesser version to Ultimate, you can use Anytime Upgrade. Type Anytime in Start Search box, insert your Product Key and it will unlock the extra features in a few minutes.
But be sure you want to use your Upgrade on a Windows 7 lesser version as there aren't that many features unlocked and you might not even want any of them. Here's a chart to compare: Compare Windows 7 Editions
It might be a better value to upgrade XP or Vista by clean installing using the Upgrade version installer: Clean Install Windows 7
If you want to get rid of your Recovery Partition, boot the Windows 7 installer to use Custom install Drive Options to delete the partitions, repartition, then Format before install.
But I would not waste the license which came with your factory OEM computer unless you know for sure
that you need the extra features, instead I would unlock all versions in the installer ISO to burn an all-versions DVD to reinstall the licensed version with Product Key on COA sticker. Reinstalling Windows 7