Hi
Do you already have photos on the new computer?
If not, then all you have to do is drag the library from the external drive into your pictures folder, and open it. If there is already an empty library in pictures with the same name, then rename it first.
Alternatively if you already have pictures in the library of the new mac, copy the old one into the pictures folder again (you might need to rename the old one first this time), open it using photos (hold down the option key while starting photos and select it) and it will be upgraded for the latest version.
Then when you open your current library you should be able to import it.
However, if you only have a few photos in the new library, you might be better off importing that (new) library into the converted library so you retain all your organisation (albums, keywords etc that won't transfer if you do it the other way around)