I think it means that the protesting group’s demands must be met, or they will continue to protest and disrupt a certain area.

We will continue protesting so loudly you won’t get any sleep.

It’s meaningless. No matter what anyone thinks or does, they are wrong. Somebody will find fault with whatever is done. No-win, no-win. (The opposite of “win-win.”)
What one person calls “justice” is what another calls “no justice.” It is all in the eyes of a beholder, or a specific mob.
You can’t have one without the other no matter whose POV is in question.
If you don’t do what we want, right or wrong, we’ll riot. Mob rule. Mob justice. Mob peace. It is chaos.

I’m answering the question about what I think the slogan means in terms of words and not what its political purpose is.

I think it’s like those signs outside a restaurant that read “No shirt, no shoes, no service” or (these days, on a bus or train) “No mask, no ride.” You can read it like this: ”(If there’s) no justice, (then there will be) no peace.”

The idea is that there can be no peace without justice. You can have the appearance of peace, but silent injustice is just war with the mute button on. This means that peace requires more than passive acceptance of injustice and/or oppression. It requires the active elimination of both of these things everywhere and for everyone. This idea that you cannot have one without the other is why the phrase is sometimes written as: “No justice, no peace. Know justice, know peace.”

What @SavoirFaire wrote.

It meas that if there is no justice we won’t have peace because there will be criminals everywhere making cities and town dangerous. Why there saying it is so the government and over people who believe in defunding the police will stop and clean up the crime that’s going on to make areas safe again and be peaceful.

Hmmm, if there are so many ways to interpret this slogan, maybe they better try a different slogan. I’ve actually seen a lot of slogans that their meaning is clear to the guys with the signs, but they might not have been tested on a general audience. Miscommunication is worse than no communication, isn’t it?

@kneesox Slogans are, by there very nature, incomplete descriptions of whatever they are used to promote. But as slogans go, this one seems pretty clear. The only two rational readings (“there can be no peace without justice” and “if there is no justice, then there will be no peace”) are inextricably intertwined. At worst, they are just different sides of the same coin.