In this part, Paul uses the illustration that an heir is in a better position than a slave to inherit an estate one day. God sent Jesus as his heir to "redeem those under the law", so "all who are in Christ Jesus might receive adoption."
Verse 4
"The fullness of the time": Paul believed and affirmed that the sending of Jesus Christ is at "the nodal point of salvation-history".
"Born under the law" means "born as a Jew."
Verse 5
"To redeem those who were under the law": means "to redeem from the 'curse of the law"', which is achieved by Christ's death "on which a curse was pronounced".
Verse 6
"And because you are sons": Some copies have "...sons of God"; the Ethiopian version reads "inasmuch as ye are his sons". God set up Christ, his Son, as the pattern for these sons to conform, by virtue of his act of grace they were considered as the children of God through Christ when he "partook of their flesh and blood", and died to gather them together who were scattered. The sons and daughters of the Lord God Almighty become the siblings of the Son of God, because through the redemption of Christ they receive the adoption as children, not as servants.
"God has sent forth the Spirit of His Son into your hearts, crying out, "Abba, Father!"": The Syriac and Arabic versions read, "our Father". All the three divine persons: God and his Son and the Spirit of his Son appear here. The same Spirit of God that moved upon the face of the waters at the creation of the world, has moved holy men of God to write the Scriptures, formed and filled the human nature of Christ, and descended on him as a dove, and by whom Christ and his apostles performed their miracles; it is called in Judaism "the Spirit of the King Messiah".
This part exposes Paul's fear that the Galatians, who before becoming Christians were enslaved to idols, now after being believers of Christ would want to be enslaved again, by meticulously observing the Jewish calendar rituals.
Paul's Perplexity (4:12–20)
The verses 12–20 display Paul's "passionate concern" for the spiritual condition of the Galatians, whom he addressed as 'friends' or 'brethren' and 'my little children', and his wish to be personally present in their midst.
This part is considered as "Paul's striking final argument" to contrast the children born of 'a slave woman', that is "to be subject to the law", with the children born of 'a free woman' 'through the promise' and 'according to the Spirit'; a contrast between "law" and "grace".
Verse 25
"Hagar is Mount Sinai in Arabia": NRSV gives the second rendering in its note, "For Sinai is a mountain in Arabia".