If you can't save your iPhone storage may be full depending your storage capacity. When your device is full, you can’t increase its storage. But you can free up space.
Go to Settings > General > [Device] Storage. You might see a list of recommendations for optimizing your device's storage, followed by a list of installed apps and the amount of storage each one uses: How to check the storage on your iPhone
If the problem is about iCloud you can check how much you are using: Manage your iCloud storage
Also check: What's the difference between device storage and iCloud storage?
Be sure to verify your iPhone video recording settings, faster frame rates and higher resolutions result in larger video files: Change the camera’s video recording settings on iPhone - Apple Support
Hope this helps and solves your question. Do not hesitate to ask if you need more information.