MacBook Pro late 2013 no longer updates to latest operating system - is it safe if I have antivirus protection?

Unfortunately anti-virus apps, cleaning/optimizer apps, and third party security software usually cause more problems than they solve since they interfere with the normal operation of macOS. Plus some of them have been caught selling people's personal information. Sometimes these third party "security" apps even create more vulnerabilities to the system.

The biggest risk is the web browser since it is accessing the Internet, especially since most web browsers are no longer supporting the older versions of macOS (this is a recent development). Most web browsers & many app developers will only support the three most recent versions of macOS. You may still find some third party web browsers which provide Long Term Support (LTS) versions that may still be supported for security updates (not necessarily feature updates).

The best thing is when the user practices safe computing habits which are outlined in this excellent article written by a respected forum contributor (make sure to read all the links within the article as well):

Effective defenses against malware and other threats - Apple Community

For what it's worth you're as well off without the AV software and just using common sense to avoid malware. Delete attachments from unknown email senders, don't pirate software or media, avoid tacky websites. That's my 2cents.

[in my opinion] unless you are a high visibility activist or politician, the protections (such as locked system volume) built into MacOS from MacOS 11 Big Sur onward mean that you will NOT be subject to any casual hacks. High-visibility activists and politicians already need additional protections.

in every case, a third-party Virus scanner as 'protection' is laughable. The idea that a third party, with no special knowledge of the inner workings of MacOS, can somehow find a simple way to protect or speed up your computer — that is not already being done by MacOS itself — suggests that the MacOS developers are somehow "holding out on you". That is absurd.

 You should remove any and all (other than Apple built-in) virus scanners, speeder uppers, optimizers, cleaners, App deleters or VPN packages you installed yourself, or anything of that ilk.

I guess if you had this third party anti virus software on your Mac you may it might have experienced the blue screen world wide IT melt down yesterday. Mac say don’t not to use Virus software in your Mac

I believe yesterday's event was restricted to the clients of one company operating only in the high-end commercial sector. That this client list is both enormous and contains many companies and agencies that impact the daily lives of ordinary people is unfortunate, as is, I suspect the future prospects for the person or team that made the error.

I did notice that BitDefender and OneDrive aren't great friends. Or at least it used to be an issue. Very high CPU during OneDrive syncs. On my late-2013 MBP 15" 750M.

And so true you wonder just how many with AV copped it yesterday with the IT melt down

if all you need is Microsoft office apps, install LibreOffice work-alike.