Tried to move photo APP onto external hard drive and now missing from comp.

Are you using iCloud Photo or did you try to move your library to the iCloud Drive?

Know that either is a syncing process and NOT off computer storage. So any change to the local library, additions, edits and deletions, will be reflected in the iCloud Library.

Do you have "Optimize Mac Storage" enabled in your Photo library?

IF NOT you can do the following to assemble all of your photos into one library on the external HD:

1 - create a new library and import all of the loose photos on the EHD.

2 - verify that the import was successful and complete and then delete those photos from the EHD.

3 - designate the EHD library as the System Photo Library in Photos' General preference pane.

4 - enable the iCloud Library in the EHD library and do not enable optimize storage.

5 - now the iCloud library will sync with the EHD library getting all of your photos into one library on the EHD. It will take a while depending on the size of the library. Some have reported up to 2 weeks or more. Just leave Photos open and in the background at night with the MacBook Pro connected via its charger and by Ethernet cable if at all possible to speedup the syncing.

6 - when done verify that the EHD library has all of the photos in it before deleting the old library or disabling the iCloud library.