I the problem is because there isn't enough room on your device then subscribing to iCloud storage won't free up space unless you also activate optimization.
In response to a similar question: "How an I get or purchase more storage space on my iPad?" (from How can I get more storage without deleti… - Apple Community ) this "clear and helpful answer" (per Solved, Helpful, and Apple recommended posts - Apple Support was recommended by Apple:
" There is no way to increase storage space. Your options would be to:
• Enable iCloud Photos to Optimize Photo storage on device
Manage your photo and video storage - Apple Support
• Delete unwanted Photos and Videos
• Review any suggested options at Settings > iPad [or iPhone] Storage.
How to check the storage on your iPhone and iPad - Apple Support
• Delete unused message threads that may contain many photos
If you still would like more storage space on your iPad [or iPhone], the only other option would be to trade it in for a larger capacity."
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I'll include this more detailed response from the same thread, though according to Solved, Helpful, and Apple recommended posts - Apple Support it is something "you don’t have to read […] to get the answers you need":
Note there's different kinds of "storage". Click on this link to discover what's the difference between device and iCloud storage, ways to manage your space, and upgrading to iCloud+ if you need more --> What's the difference between device storage and iCloud storage? - Apple Support
Take-away:
1. Storage on a device itself is fixed and cannot be upgraded except at the time of purchase. If you want that then you have to change your present device for one with more capacity.
2. iCloud storage is on Apple's main computers. It is not a like a normal storage hard drive but by using optimization settings on your device it can help free up device storage. Lesser used items and larger file versions can be stored in ICloud and you can get access while connected to the Internet. It does not turn a 64 GB storage device into a 64 (or whatever) + 50GB/200GB/2TB device but if you have a lot of things that aren't being used much, or you don't mind only having lesser quality photos on your device, it can free up extra space so you can make the best of the GB you do have on the device itself.
If you have upgraded iCloud storage and are seeing a message on your device that storage is full then it is possible you are not making the best use of iCloud storage and need to use optimization features. If you do have optimization activated then it is possible you are exceeding your device's needs in terms of on-device storage and you need to buy a device with more storage.
Click on the link to learn how to optimize the storage on a device --> "How to check the storage on your iPhone, iPad, and iPod touch" - How to check the storage on your iPhone and iPad - Apple Support
- "If your device is low on storage, it automatically frees up space while installing an app, updating iOS or iPadOS, downloading music, recording videos, and more.
To make more storage available, your device can remove some of your items, like streamed music and videos, files in iCloud Drive, and parts of apps that aren't needed. It also removes temporary files and clears the cache on your device. But your device only removes items that can be downloaded again or that aren't needed anymore."
Here's the same information as a video: "How to free up space on your iPhone, iPad, or iPod" - https://youtu.be/bnhuHSv_WrI
Optimization specifically with reference to "Set up and use iCloud Photos" - Set up and use iCloud Photos - Apple Support
--> Save space on your device
iCloud Photos keeps all your photos and videos in their original, high-resolution version. You can save space on your device when you turn on Optimize Storage.
Manage your photo and video storage - "Learn how photos and videos use your iPhone, iPad, and iPod touch storage, ways to save space, and how to upgrade your iCloud storage if you’re running out."
Manage your photo and video storage - Apple Support
Another way to free storage on a device is to transfer items to a computer and move them to locations which are not part of iCloud so they won't just sync back again. The items are archived on the computer and on backups you make of the computer. Read this article to learn how to sync your iPhone, iPad, or iPod using your computer - Sync your iPhone, iPad, or iPod using your computer - Apple Support