If there isn't an update listed within the tablet "Settings" area, then there isn't an update.
You could try other means (rooting) of putting a newer OS on the device, but there are no guaranties it would work. Then there is the possibility that your device wouldn't be able to function well with a newer OS due to the requirements of it (kind of like trying to put Windows 10 on a machine made 10 years ago). While it may accept the installation, it will never run well. Plus there is the possibility that making said change could also brick the tablet. Personally I am not a fan of rooting.
Also, anything you had on the tablet would be lost, due to it not being a standard tablet update. Apps, photos, music, etc., all gone. It would be smarter to purchase a newer device with the Android version on it that you want to use/have. Just make sure it isn't a device that the manufacturer has restricted that option on.
Now if you are just trying to make room, you could move all your photos, music, videos, etc., to the SD card and that would free up a lot of space. Then I would suggest uninstalling any apps you really don't use. After that is done, go into the "Settings" then "Apps" and locate apps you use all the time, and clear out the cache. Just make sure it isn't one you need the info for like oh your contacts.
The choice, obviously, is yours.