There is no need, just point to the new library in this project -Setup - Settings - Project and change the Central Library Path to the new project. To ensure everything still works copy the parts from the original library to the new library and use the same partition names. If the partitions don't exist create them in the library using Library Manager - Partition Editor.
All you are doing with the project templates when you create a new project is pre-defining some of the settings such as the library location, you can easily change these later if they don't suit your requirements.