“this connection is not secure” in Safari

I am regularly getting the error message “this connection is not secure” when trying to follow a link to a website in safari.

Most recently to a website to set up an account for some finance I got when I bought something - meaning I don’t dare use that website. Then this morning to the local Nub News site.

I’m pretty sure they’re not phishing emails.

I’ve heard this might be linked to Apple changing how new they expect certificated to be but this could be rubbish.