After the trial has ended and I have decided to purchase Logic Pro, do I need to re-download and reinstall the Library?

Hi there,

According to this link, you should reinstall:

When I purchase Logic Pro from the Mac App Store or the trial expires, what should I do with the Logic Pro trial application?

You can remove the Logic Pro trial after it expires. To delete the Logic Pro trial, locate the app in the Applications folder in the Finder, drag the app to the trash, then choose Finder > Empty Trash. 

You can also remove any Sound Library content you might have downloaded. Choose About This Mac from the Apple menu, click Storage, then click the Manage button for your system storage drive. Content for Logic Pro (as well as other music creation apps, including GarageBand and MainStage) is listed in the Music Creation section. You can view the capacity of the Instrument Library and Apple Loops library and delete each of these items. If you delete content you downloaded with Logic Pro, you might have to download the content again for use with GarageBand.

Link: https://support.apple.com/en-us/HT211113

Hope this helps and solves your query,

Eddie G.

You are most welcome.

Hope this helped and solved your query,

Eddie G.