Hi!
No, you shouldn't. Just install the Pro version on top of the Core version, without uninstalling. Note: if you don't see the extra features, you may have to install the Pro version again, without uninstalling. This is a Joomla! quirk, caused when two component packages have the same version number but different number of files (this is the case with Core and Pro packages of Admin Tools).
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!