Do you intend on continuing to use iPhoto with Sierra? It will have to be version 9.6.1. If so do the following:
1 - rename and copy the iPhoto library from your old Mac to your new one.
2 - open the old library with iPhoto on your new Mac to convert it to the same version as your current library on the new Mac.
3 - purchase the paid version of iPhoto Library Manager and merge the older library into the newer library.
NOTE: be sure to have a backup copy of your current library on the new Mac before starting the merge.
4 - After the merging is complete verify that you have all of the photos in the library before deleting the library from the old Mac.
If you intend to use Photos as your photo management application continue with the following:
5 - migrate your merged iPhoto library to Photos by opening it with Photos.
