"No Justice, No Peace" is a slogan, more often a chant, which has been used by protesters in the United States, it seems, since the eighties.
This chant was first recited by crowds protesting the murder of Michael Griffith by a mob of white youths in Howard Beach in 1986.
In a 1987 interview with the New York Times, Sonny Carson explained the chant, as it related to his protest philosophy, saying
"You don't give us any justice, then there ain't going to be no peace. We're going to use whatever means necessary to make sure that everyone is disrupted in their normal life."
This, to be sure, seems to be how the chant is used now, into 2020. "No Justice, No Peace" is yelled as a threat: "If you continue to deny us the justice we demand, then we will continue to make noise, denying you your peace." But this is not the only, nor should it be the chief, meaning behind the chant. Martin Luther King, Jr., likely inspired by Isaiah 32:17, proposed in his speech called Sir, You Don't Know Me. (1968) that
"There can be no justice without peace. And there can be no peace without justice."
And, while taken at face value, King seems to be merely proposing an inherent solidarity between the civil rights and anti-war movements, the connection can go deeper. King did not say "there can be no peace movement without a justice movement". He referred to peace itself and justice itself. King was observing that a world with injustice will never permit its inhabitants to live peacefully. Even in a state of apparent order, there will be war and tumult on people's hearts. Conversely, if there is not peace in the world, then one must look to the injustice to bring that peace about. If we accept this link, then a way to define these two concepts in terms of each other while capturing the connection King was going for is this:
Peace is the tranquillity of justice.
The chant "No Justice, No Peace", then, is converted from a threat into a statement of fact.
And this I tell you, brother: you can't have one without the other.