This may assist you as you think about what it means to live under the Law.
1. It’s not possible for a Christian to be a Pharisee without first rejecting Christ. If a believer imposes personal convictions that go beyond the Scripture on other believers, he may be unloving and without understanding, but he isn’t a Pharisee.
2. Living by the letter of the Law versus the Spirit of the Law is not a biblical dichotomy. Paul isn’t speaking about a rigid versus flexible use of the Law. Rather, Paul contrasts living by the Law (living under the Mosaic Law of the Old Covenant) with living by the Spirit (the way believers are to live in the New Covenant).
3. Living under the Law isn’t the idea of doing good works that you believe might save you, but living by the Mosaic Law code, especially in its externalities (such as practicing circumcision, feast days, separation from Gentiles, Sabbath laws—for purposes of justification). If someone says to you, “You must be circumcised to be saved” (Acts 15:1), you’ve encountered a first century Law issue.
4. Paul appeals to Gentiles to avoid going under the Mosaic Law for many reasons, two of which are these: they were never obligated to be under it in the first place, and they had their own “elemental principles” (i.e. religious rules and ceremonial rituals) in their former pagan religions which should teach them not to go that way.