Can justice and forgiveness go hand in hand? and why?

Since forgiveness and justice are very wishy washy terms that can be easily stretched every which way, I will use the textbook version.

Justice is defined as creating fairness.

Forgiveness is the act of forgiving. Defined by psychologists, its a deliberate decision to release emotions of anger and resent towards a person/group/idea that hurt you.

So yes, you could forgive someone and place justice. It's like a mother making her child sit in the corner for ruining the carpet; she's not mad but she still gives her child a fair punishment to how them what they did was wrong.