Hall of Fame
The words you quoted of Paul were spoken in defense of the charges against him that he was a mover of sedition among the Jews (Acts 24:5). Paul said that what he was teaching to the Jews came straight from the OT and therefore he did nothing wrong.
The gospel Paul preached to the Jews was based on what the prophets foretold (Ro.1:1-2) while the gospel which he preached to the Gentiles was bases on truths that had not been revealed and had been kept secret:
"But we speak the wisdom of God in a mystery, even the hidden wisdom, which God ordained before the world unto our glory: Which none of the princes of this world knew: for had they known it, they would not have crucified the Lord of glory" (1 Cor.2:7-8).
The Gospel that Paul preached was given to Him by revelation from Jesus Christ.
Galatians 1:11-12 New American Standard Bible (NASB)
Paul Defends His Ministry
11 For I would have you know, brethren, that the gospel which was preached by me is not according to man. 12 For I neither received it from man, nor was I taught it, but I received it through a revelation of Jesus Christ.
And this is the gospel he preached.
1 Corinthians 15:1-4 New American Standard Bible (NASB)
The Fact of Christ’s Resurrection
15 Now I make known to you, brethren, the gospel which I preached to you, which also you received, in which also you stand, 2 by which also you are saved, if you hold fast [a]the word which I preached to you, unless you believed in vain.3 For I delivered to you as of first importance what I also received, that Christ died for our sins according to the Scriptures, 4 and that He was buried, and that He was raised on the third day according to the Scriptures,