I moved my iphoto library to an external hard drive. I then updated my macbook air to the new OS X operating system. The new "photos" app now says it doesn't have permissions to connect with the external hard drive. How do I link the two?

Check the file system of the external drive and enable the "Ignore Ownership on this volume" flag. That will help with permission problems.

The file system should be MacOS Extended (Journaled), as described in this support document for iPhoto: iPhoto: Sharing libraries among multiple users

Is your external drive directly connected or remotely mounted?

How is the EHD connected to your Mac? What format is it?

And why did you move the library - Upgrading you OS does not require moving the Photos library?

LN