No need to install it dude just enter the new Serial number into service center and it will change TP2 to TSP2 and all your stuff (playlists etc) will remain.
Assuming that you are on the latest version. Your sig says not ?
You canโt have copies of the same version in your machine, for Service Center itโs only 1 program. Another story is if you were running Pro1 along SPro2.
Basically you are upgrading your license doing what Karlos said.