就要 normally means "about to" but in this sentence the negated form makes the sentence hard to translate.
过去的事情就不要说了 means it's not necessary to mention those things in the past. Or it's not deserve to mention the things in the past. It implies that just let it go because it is just meaningless/helpless to the current situation.
就 here is kinda like the word just. So, 就不要 here is kinda like just don't because there is no use.
You should comprehend 就不要 as 就 and 不要 in this case. 不要 is like "don't" in an imperative sentence. For example, 不要说话: don't speak! 就不要说话了 is kind of suggestion, meaning just don't say anything.
Another point is 过去的事情就不要说了 can be paraphrased as 就不要说过去的事情了. By pulling 过去的事情 ahead, it's like saying: things passed, so just don't mention it.
就要 doesn't always mean "about to", it can mean "have to". Here's an example
where 就要 means "have to". (The whole sentence is "If you want good grades you have to work hard)
In your sentence, 就要 is negated from "have to" as "don't have to". The whole sentence translated would be
You don't have to talk of the past things.
不要说了 means "don't talk about". 过去的事情 means "past stuff" or more idiomatically "the past". So 过去的事情不要说了 means "don't talk about the past/past events".
The 就 is a grammatical particle that doesn't really change the meaning of this sentence significantly. The translation of the 过去的事情就不要说了 (including the 就) would be the same as what I wrote above for the same sentence without the 就.
If you want to learn more about the uses of 就, there are many good articles and blog posts you can find on google.