Make personal Photo Library default for new photos

If your question relates to photos taken on your iPhone, check Settings > Camera > Shared Library > Share from Camera on your iPhone. It controls where the Camera app places new photos it takes.

If the new photos are arriving some other way or from some other device, please let us know.

In Photos' Gemeral settings pane set your personal library to be the System Photos Library:

All new photos will go into the System Photos Library.