Hi
Is it a photos library on your external drive? Or an old copy of the photos app? The app doesn't hold your photos, the library holds it. If it is a crossed out app, it will be from an older version of MacOS and not able to open with this version. Is there also a library on the external drive?
If not you need to copy the library from your old mac - normally called photos library.photoslibrary (assuming you've not renamed it or created a second library) and normally stored in the pictures folder. Your new version of photos can open and upgrade the library from the old version.
Regarding the external drive - is it correctly formatted for a photos library?
It must be formatted APFS or MacOS extended (journaled) (preferred for spinning drives). If you have not formatted it after purchase it will most likely be ExFat - which is not compatible.
It Must not be (or have been) used for time machine. (A time machine drive can be used if re-formatted)
It must have the 'ignore ownership" checkbox ticked.
It must be directly connected (No ethernet or wifi)
See
https://support.apple.com/en-gb/HT201517