I have a macOS catalina version 10.15.7, can i update my mac without purchasing a new one ?

Which version you can update to is 100% dependent on your Mac model (and year). Without knowing that, no one can answer the question.

Your profile lists an 'iMac 21.5"', but there are many of those, released just about every year from 2009 through 2019.

Generally, the App Store will offer the latest version compatible with your system, but to be sure, check 'About This Mac' from the Apple menu to find the specific model and year. Then you can use the links on Find out which macOS your Mac is using - Apple Support to find which version is the latest you can support.

Back up your data, check the application compatibility table, click here, and if your iMac is a mid-2014 or newer model, then on the download link for a more-recent OS.

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