It's completely unnecessary. You can just use your new serial number on the trial and it will turn into the full version.
But, otherwise, you're welcome to just uninstall the old and reinstall the app.
You don't say what operating system you're on, but if you're on a Mac, you should uninstall using the uninstall program in the Premiere Elements application folder.
From what I have read the Mac Store is selling at least two variations of Premiere Elements 11 for Mac
Adobe Premiere Elements 11 Editor (Mac Only)
Adobe Premiere Elements 11 Quick Editor (Mac Only)
Did you buy either of those which are described in the following Mac Store product comparison
Depending on your reply, you should check with the Mac Store to make sure that you do not have a serial number
there waiting for you to use.
Here is my take on your situation.
If you have the Premiere Elements 11 Mac tryout on your computer and it was downloaded from Adobe, you do not have the same program from the Mac Store under the name Adobe Premiere Elements 11 Editor (Mac Only). This Mac Store version of the program comes without the Elements Organizer 11.
So, I would review the wisdom of plugging a Mac Store purchased serial number into your Adobe tryout under the circumstances. I am not on firm ground here. But, if it is I suspect and you want what you purchased, then consider uninstalling the Adobe tryout and installing what you purchased from the Mac Store with the serial number that the Mac Store gives you.
I would ask Steve Grisetti to double check on this point before you proceed with the computer setup.
Did you realize that the Elements Organizer was not a part of the Mac Store version?
Thanks for the follow up.
Thanks for your attention. Yes on my computer I have both, the trial version of Pre
Elem 11 downloaded from Adobe and the same app from Mac Store. You are right the Adb Pre Elem 11 Editor (from MacStore) doesn't have the Organizer 11. I could noticed that just after I had already bought it.
I have sent an email to Apple support asking for my serial number, the answer will take one or two days.
I think ATR has hit on an important point. The App Store version of Premiere Elements appears to be different than the full version.
So it may be wise to uninstall the free trial before loadig the App Store version.
As I said in my first post, you can uninstall the program by selecting the Uninstall program from the Premiere Elements folder in your Applications.