How can I upgrade my old Mac without buying a new one?

Upgrading drives or RAM will not change the maximum version of macOS that you can run. If that 21.5" iMac has a hardware model year of Late 2012, Early 2013, or Late 2013, Catalina is the end of the line, No upgrades to Big Sur, Monterey, Ventura, Sonoma, Sequoia, Tahoe, or Golden Gate would be available.

Catalina hasn't received the latest versions of Safari for several years, and isn't enough to run current versions of most major third-party Web browsers. For the moment, it is still good enough to run Firefox.

You've learned that your 21" iMac has reached the end of the line as far as upgrading the system.

It the iMac is doing what you want it to do currently you don't need to think about upgrading or a new Mac.

However, if it won't do what you need and that will require a new Mac consider the following:  a 12‑core CPU, 12‑core GPU Dual 16‑core Neural Engine Mac Mini M6 with 16 GB RAM and 1 TB SSD ($1399 US) with a 32" LG 4k monitor ($331 US) from Amazon.com)  is $1716 which is $450 less than a similarly configured new 24" M4 iMac ($2199 US). Keep your keyboard and mouse from your current Mac for use with the Mini. If you recycle don't include the mouse an keyboard.

I got the previous Mini M4 with a 32" LG 4K monitor w/speakers for the same price as a 27" monitor (didn't know the Mini had a speaker).  There are many monitors available in 27" size for about $100 US to $500 US depending on what features you want.  I love the extra screen real estate of the 32" monitor.

I had an 2017 i7 iMac with an SSD boot drive and a new M4 Mini runs circles around it.  The new M6 will be even faster.   

You can use the keyboard and mouse from your current iMac. Don't include them with the iMac if you use Apple Trade In or recycle with the iMac.

Just some food for thought.

iMac Intel 21.5" Upgrades - iFixit , is the website that will guide you with every upgrade you want. I got this result from https://duckduckgo.com/?q=imac+iMac+21.5+catlina+pyshical+upgrades&kp=1&t=osx&ia=web

Current versions of Linux and one or more of the BSD UNIX variants will install and work on most Intel Macs.

This won’t be macOS, so you’ll want to be sure you have equivalent apps available for your particular computing requirements. Mail, web browsers, LibreOffice, etc., are all available.

For what you ask, probably the elementary OS Linux distribution.

If your hardware is from 2013 then you have reached the end of update.

Check menu and tell us what you have

 > About This Mac > under iMac the model & year

If it is from

2013 update to Catalina

2014 update to Big Sur

2015 update to Monterey

2017 update to Ventura

...

To sum up all the suggestions posted here, why don't you

• Buy a new Mac
• Use it as a Linux machine like Linux Mint
• Or your questions' answer: Duck duck go search imac 21.5 inch Mac os 10.15 and if you want to upgrade on your own (or else you don't have any other upgrading options because shops won't upgrade, neither Apple), then iFixit iMac Intel 21.5" Upgrades - iFixit

Hello,

The short and honest answer: you can't just upgrade, you need a new one to upgrade. Depending on your model and how you use your device, I can suggest a new one for you, if you want.

Thanks

Yeah, I agree, lets be realistic. Move to linux, or just get a new Mac, why overcomplicate it?

My bad English, is not enough here I see....

Why not upgrade to LINUX?

See, some apps depend on technology; if that's the case and the computer is the main device he uses, he will upgrade it. He might have purchased old Mac apps, which depend on it.