What versions of macOS you can run on my Mac from late 2013 - now it's Catalina
Will I have to buy a new MAC to be able to install newer versions and is worth doing that ?
iMac 21.5″, macOS 10.15
Question marked as
Catalina is the last version that iMac model can update to. It lacks the hardware for anything newer.
Yes, you will need a "newer" Mac to run a newer macOS version.
Wether it's worth it or not to you depends on your requirements. If you have apps that no longer work and will require a newer version of MacOS and you absolutely cannot work without them, then yes, it may be worth it.
If you can still do everything you need on Catalina, then probably not worth it to get a new Mac. It would be a good time to start saving up for a new one in the not to distant future anyway though.