What do you do when the Apple Mac fails to recognise the mouse despite fitting new batteries

Hey Malcolm,
I know that it can be frustrating if your mouse is not pairing with your iMac. Let's see if we can get it sorted out.
Start with the article below and look at the first section for mouse or keyboard not recognized by your computer. It will have you check to make sure devices have power even though you just replaced the batteries.
Troubleshooting wireless mouse and keyboard issues
https://support.apple.com/en-us/HT204621
Take care

Just because you have new batteries does not mean you have power. Is the green light showing? What did your last batteries die of. Exhaustion? Were they leaking? If so, have you cleaned the terminals inside the battery compartment?

I am a little surprised at that, Malcolm. 'Only a year old' is no time at all ... 3 to 4 years perhaps but I suspect they may have wanted the business. Did you keep the old one and did you check the points I made? If you do and discover it is reparable, take back the new mouse for refund. I still have a USB mouse from 2007 and a Magic mouse from 2010. Both are in a good state and working effortlessly.