I'm understanding that you have photos being synchronized between 2 different systems - what is the purpose of doing this?
You are looking to add a new drive to your main PC due to lack of drive space - ok. Easy enough to add a second HDD to your system.
Now are you looking to move the original storage location of these pictures or change the sync'd location of the pictures? Either one can be done with ease.
Install your second HDD in your main PC. Then, if you still need to sync the files, setup Offline Files and choose the location of the new drive. If the files are currently setup to sync to your primary drive on your main PC, then delete those files and the Offline Files task for that primary drive so the files are no longer syncd and taking up space on that drive.