There are two different views of the law being a “School Master”
1. This man was like a truant officer who made sure children attended school. Being Under The Law - Dealing with the fear of the law
2. This man was a Tutor to teach moral and social behavior. Torah - Teacher or Rabbi
In Galatians, Paul mostly refers to the First type, except when he mentions The Law of Christ, or to Love our neighbor in Gal 5:14, 6:2.
3:15-18 Abraham was Justified by Faith - Faith is a KEY concept in Galatians as noted later
3:19-25 The Law was a schoolmaster leading us to it’s goal - Who is Christ (the Messiah)
3:28 In Christ, There is no Jew nor Greek, no bond nor free, no male nor female - All are One in Christ and Abraham’s Seed, as was promised to all the nations through The Seed.
This is the basis for The New Age or New Testament - Jesus' death removed the Old and His Resurrection Established The New Life....
4:9-10 You were Gentiles observing (pagan) days, months, times and years when you ‘Knew Not God.’ Here is the ditch on the opposite side of the narrow road. On the one side we have Judaism and on the other Paganism. Both offer ritual, ceremony and tradition, but the truth lies in the narrow way.... We can see the Differences in the NT vs OT Law .... BUT in Paul's early ministry there was only Acts 15 as the New Standard. No Circumcision and No Idols nor fornication - Eating blood or strangled animals was also excluded....
The OT is a natural provision for a natural people - though God showed His Power in Egypt and Sinai to enable The Covenant. While in the NT we see Christ died a natural death BUT Rose in Spiritual Power and The Holy Spirit was poured out at the End of The 7 Weeks on The 50th Day like a Jubilee - freedom event...
Under The Law - is being a debtor bond-servant and not a free-man. This better fits most of what Paul has to say in Galatians, including the Hagar picture. Thus Under Debt to The Law - and because sin reigned they always were in debt....