According to this from FAQ:
Am I able to directly install new PD7 over PD6, and it will accept my new key?
Thanks
3.How do I activate Parallels Desktop 7 for Mac?
New customers: You can activate Parallels Desktop 7 during installation. If you choose to activate after installation, go to the Parallels Desktop menu and select "Activate Product".
Enter your name and the other requested information plus your activation key for Parallels Desktop 7 for Mac in the activation form and click 'OK'.
Upgrade customers:
Parallels Desktop 5 and 6 for Mac customers:
If the Parallels Desktop 7 for Mac Upgrade installation does not automatically detect the previous version key, enter your activation key for your previous version of Parallels Desktop (either version 5 or 6) in the pop-up window and press 'OK'.
To find your previous version key refer to this article.
Am I able to directly install new PD7 over PD6, and it will accept my new key?
Thanks