Galatians 4 continues the thoughts from 3 but puts a little different flair to it. The essence of the section is our relationship to God is closer than we might think. Additionally it is established and sustained differently than most pursue it. Some would say chasing after the law is something that was done in the past, you know in Jesus day. The reality is, we are still chasing the law, we have simply exchanged the laws we are chasing.
Part of the human condition is our propensity to codify and organize, to create boundaries and rules for ourselves and others to follow. This in and of itself is not a bad thing. Trouble enters the picture when we begin to hold up this order and rules as the primary, and push God to the margins. Many titles have been given to this process, some call it legalism, others call it orthodoxy. The reality is when the rules and organization become more important than God it is simply one thing, sin.
Since the incarnation in Jesus, God has removed the rigidness of the rules and we no longer live bound to the law. This does not mean however, that we are boundless and free to do whatever we want. We live under grace, which means we have the freedom to follow Christ will all our being. We have the freedom to live like and for the Kingdom of God. We so not have to live like the rest of creation, rather to work on living like creation was intended.
This is what Paul is reminding the church in Galatia, as well as you and I. We are not children of slavery, we are children of the promise when we place our life in trust to Jesus Christ.