How do I install the latest Apple update on an older Mac without purchasing a new computer?

Joelbira wrote:

how can I install the latest Apple update without purchasing a new computer

I am on Version 10.15.8 Catalina and it will not update any further - can I purchase SSD - will that work or any other suggestions please?

Purchasing a SSD will not let you run more recent versions of macOS.

If your 27" iMac is running Catalina, and refuses to offer you any later version, that implies that it is a Late 2012 or Late 2013 model for which Catalina is – and will always be – the end of the line. To run macOS 26 (Tahoe) - an OS which is six major versions ahead of Catalina, you will need to purchase a new, or at least much newer, computer. That computer should have an Apple Silicon processor (preferably a M4- or M5-family one). There are a few Intel-based Macs that can run macOS 26 (Tahoe), but none of them will receive macOS 27 (Golden Gate) when it comes out this fall.

Catalina does not support the current versions of Safari or even of most major third-party Web browsers – with one exception. The current version of Firefox still runs on Catalina, so you might want to keep a copy of Firefox on hand while you plan for this iMac's replacement.

Sorry, but no. It is the hardware (CPU, GPU, etc) on your computer that is not capable of running any newer version of MacOS. An SSD is just for storage and would be helpful if you are seeing an error that there is not enough space available on the computer to install the update, and in that case you would move files from your computer to the external drive to free up the space.

But if you see on your computer when going to Software Update, that there is no update available, then you have reached the end of line for that computer as far as updating to another version. You may still receive point updates to Catalina for security patches.

You cannot upgrade to a newer OS version than your Mc can run without buying a new computer. If your Mac is not on a list of compatible computers, then there is no further upgrade path for that machine.

These are the Macs that are compatible with macOS 11 Big Sur, the version that superseded Catalina:

➡️ macOS 11 Big Sur is compatible with these computers

These are the Macs that are compatible with macOS 26 Tahoe, the current version of the OS:

➡️ macOS 26 Tahoe is compatible with these computers

If you find you'll need to get a new Mac in order to run your apps consider the following:  a 10 Core Mac Mini M4 with 16 GB RAM and 1 TB SSD ($1299 US) with a 32" LG 4k monitor with speakers ($318 US from Amazon.com - this price is befor tarrifs and the Strait of Hormuz) is $1617 US which is $582 less than a similarly configured new 24" iMac ($2199 US). 

I got the above Mini 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.  e tax, tariffs and the Strait of Hormuz.

I had an 2017 i7 iMac with an SSD boot drive and the new Mini runs circles around it.  So much faster.  

You can use the keyboard and mouse from your current iMac. Don't recycle them with the iMac.

Just some food for thought.