Those battling addictions understand turning from evil and doing good. Yes, it's imperative to turn away from that life and begin to live a good life--one that is filled with choices that honor God and honor yourself.
But this verse tells us to actively seek peace and pursue it. To me, there is nothing passive here. We could casually look for peace when it seems like it fits in our schedules. But to pursue means to make it actionable - like all the time.
Thing is, what do you consider peace? After today, I would consider it "peace" if my kids would just get along for more than 5 minutes. But honestly, peace means different things I believe to what's going on in your lives.
So perhaps peace means finally accepting that you will no longer return to your addiction (and that's huge..so I'd say make some not so peaceful noise to celebrate that one). But, perhaps it means working through the steps, or making peace with others you have hurt, or after being turned away from those who choose not to forgive you..coming to peace with that. See, having peace while working through the steps will happen but it takes action. And it is hard work.
Wishing you some peace today!!