You can certainly keep your photos on an External Hard Drive (EHD).
Firstly, you can copy your Photos Library to an EHD. Then, on your Mac, tell it where the Library is. When you confirm that the Library on the EHD is okay, you can delete the Photos Library on your Mac to save space.
This Apple article explains all the details regarding running your Photos Library from an EHD.
To save storage space on your Mac, you can move your Photos library to a different storage device.
support.apple.com
Read it carefully and bear in mind that running your Photos Library from an EHD, means that it is the only source of all your photographs. You might therefore consider copying the contents of that EHD to another EHD from time to time as a Backup (BU).
Secondly, you can BU all your photos to iCloud assuming you have enough space in iCloud - or you can purchase more space if you need it.
Anything not clear, or if you want more info, please post back.
Ian