If you've already purchased the extra "iCloud Storage" then the data on your device that's associated with iCloud (Any photos, videos, files, calendar events, reminders, notes, etc.) will auto-sync to iCloud according to the available storage.
But "buying more storage" on iCloud will not free up space on the device itself.
If you want to remove photos etc. from the device, you should back them up to an alternate service (Dropbox, OneDrive, etc.) and then delete them from the device.