Trying to update on old computer to OS 10.15 have OS 10.13
Prefer not to buy whole new computer if not necessary.
iMac 21.5″, macOS 10.13
Question marked as
What happens when you try?
Do you have a good backup or two?
Which exact Mac do you have. Apple logo at top left>About this Mac…
MacOS Catalina 10.15.7 - Technical Specifications
General Requirements
OS X 10.9 or later
4GB of memory
12.5GB of available storage (OS X El Capitan 10.11.5 or later)*
Some features require an Apple ID; terms apply.
Some features require a compatible internet service provider; fees may apply.
Mac Hardware Requirements
For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:
MacBook (Early 2015 or newer)
MacBook Air (Mid 2012 or newer)
MacBook Pro (Mid 2012 or newer)
Mac mini (Late 2012 or newer)
iMac (Late 2012 or newer)
iMac Pro (2017)
Mac Pro (Late 2013 or newer)
How to download and install macOS - Apple Support
https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12
macappstores://apps.apple.com/app/macos-catalina/id1466841314?ls=1&mt=12
How to upgrade to macOS Catalina – Apple Support
And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...
https://www.stclairsoft.com/Go64/
And lastly, why do you want to upgrade???