The allegory of Hagar and Sarah is often cited as representative of the distinction between "law" and "grace" in the writings of Paul (Gal. 4:21-31). Sadly, many traditional Christian commentators have used this allegory as a means of rejecting the importance of Torah study for the Christian. I don't have the time to go into this subject in depth presently, but I will at least touch on the theme here. Hopefully you will see that it is overly simplistic to consider Paul's use of this midrashic technique (i.e., the use of allegory) as an argument against the Torah and its significance in our lives.
As taught in parashat Vayera, Abraham had two sons: Ishmael, the son of the slave Hagar, and Isaac, the son of Sarah. Ishmael's conception was "natural," i.e., was "of the flesh" and the result of human intervention and calculation; Isaac's conception, on the other hand, was supernatural and the result of God's miraculous intervention and design.
The Apostle Paul interprets these historical events in allegorical terms. The two mothers "represent" two distinct covenants: Hagar (who, according to midrash was the daughter of Pharaoh) represents the covenant made at Sinai that results in "children born of slavery," whereas Sarah represents the covenant made earlier based on divine promise that results in freeborn children (Gal. 4:24-27). Mount Sinai is in the barren wilderness -- the starting point of a nation that was once enslaved in Egypt; but Mount Zion/Jerusalem (representing the fulfilled promise) is in the "land flowing with milk and honey" -- the ending point of a nation that is divinely elected. Mount Sinai is ultimately barren, but Mount Zion is "the perfection of beauty" (Psalm 50:2) who bears innumerable children (Isa. 54:1).
It should be remembered that Paul's idea that Hagar and Sarah represent "mothers of two different peoples" can easily be misunderstood (2 Pet. 3:15-16). Historically, many traditional Christian commentators have used the allegory as a means of rejecting the importance of the Torah and engaging in hateful anti-Semitic rhetoric. It is clear, however, that Paul had the highest regard for the revelation at Sinai and positively upheld the law (Gal. 5:14,22; Rom. 3:31, 7:12, etc.). He never renounced his Jewish identity and even called himself as a Pharisee after engaging in missionary work among the nations (Acts 23:6, 25:7-8, etc.). I think that Paul's point can be clarified if we remember the vital distinction between the idea of covenant and Torah (for more on this, see Olam HaTorah).
Based on the overall context of the letter to the Galatians, we understand the allegory as a means to impugn the authority of "Judaizers" who claimed to be the Torah's exclusive interpreters. Physical circumcision (as the "prototypical" work of being a Jew) is not a means of salvation, and any attempt at "justification" based on personal merit is a step away from that which comes freely to those who trust in the divine promise of eternal inheritance. The doctrine of "justification by grace through faith" is a fundamentally Jewish concept, amply illustrated and taught in the Torah. Indeed all acts of revelation from God (including the revelation given at Sinai and the Cross at Moriah) are manifestations of Divine Love. Salvation is "from the Jews" (John 4:22), and God has promised that there would always be a remnant of His people who would believe (Isa. 1:9, 10:21, Jer. 23:3, 31:7, Joel 2:32, Rom. 9:27, 11:5, etc.). In the end, "all Israel shall be saved" and all of the divine promises given to the Jewish people through the prophets will be fulfilled (Rom. 11:26).
The new covenant of Jerusalem (Zion) was prefigured at Moriah - and harkens back to Abraham and Isaac - not the later covenant made with national Israel at Sinai. The children of Zion are the children of promise, and the covenant "cut" in the Person of our Mashiach opens up Zion to us all... "Torah" ("instruction," "direction," "aim") is a functional word that refers to man's proper response to God's covenantal actions in history. We do not impugn the Torah when we say that God has made a better covenant based on better promises (Heb. 8:6). The LORD is the same yesterday, today, and forever: He is one.... The revelation and grace of God is manifest at Sinai as it is at Zion. What's changed is the covenant -- and our response to that new covenant in light of the full counsel of the Scriptures. An honest reading of the Book of Galatians shows that Paul was not simply rejecting legalism, but any form of work-based salvationism. Israel should have known this, since the Torah (and prophets) prophesied that a new era of "circumcised hearts" would come. Therefore Paul puts forward the idea that salvation by the grace of God is in perfect harmony with the teaching of Torah.
As for Hagar, it must be remembered that God "blessed Ishmael" and promised to make him the father of twelve tribes with innumerable offspring (Gen. 16:11; 17:20). According to Rashi, the sacrifice of Isaac was middah keneged middah ("like for like") justice applied to Abraham's unjust dismissal of Hagar and his firstborn son. After all, despite his wealth and power, Abraham had sent them away to a certain death in the desert.... Indeed, Isaac later seemed to understand this, and many of his spiritual encounters with God occurred at Beer-lehai-roi, the place where Ishmael was first named - and later abandoned. According to Jewish tradition, Hagar was renamed as Keturah and later married Abraham after the death of Sarah. Both Isaac and Ishmael buried their father -- together -- at the Cave of Machpelah (Gen. 25:9). All this interconnection indicates that there is a future and a hope for the descendants of Hagar - both the physical descendants as well as the spiritual ones. God will hear Ishmael! We should remember the Arab peoples in our prayers, chaverim...
Note: Abraham has more identifiable descendants than any other person in history... From the line of Isaac would come the twelve tribes of the Jewish people, and from Ishmael would come the twelve tribes of the Ishmaelite people. Abraham also later married Keturah who bore him six more sons that became founders of six other nations of the Arab world, including the Midianites. To signify Abram's status, God changed his name from Avram ("exalted father" [from אָב, "father," + רָם, "exalted"]) to Avraham ("father of a multitude," a homonymic wordplay from אָב, "father" + המוֹן, "crowd"). Notice that some regard Avraham's name to mean "father of mercy" (from אָב, "father" + רחם, "womb").