2:1-9 What was the gospel that Paul preached which he communicated privately to the leaders of the Jerusalem church in V2?

The gospel Paul communicated privately to James, Peter and John etc. in the Jerusalem church was the same gospel Peter and the other preached to the Jews - the gospel of grace.

This passage does not teach, as many in the church believe, that there were two different gospels at that time - one for the Jews and one for the Gentiles.

It simply means that God had delegated to Paul the responsibility of taking the gospel of grace to the Gentiles, and to Peter, the responsibility of taking it to the Jews. (cp Ac 15:1-12).

This proved Paul's equality with the apostles at Jerusalem; that he was recognized by them in his apostolic authority.

Paul's fear that those in authority in the Jerusalem church might thwart his past and present efforts to establish a church free of all old covenant ceremonial rituals was groundless.

The apostles together with the elders and the entire Jerusalem church agreed with his gospel completely and prohibited the Jewish Christians from trying to impose the law of Moses upon the Gentiles (cp Galatians 2:2 with Ac 15:22-31).

Paul's meeting with the apostles in the Jerusalem church was a milestone in Christianity. It resolved the doctrine of salvation by grace through faith alone.

Until the question of Gentile circumcision was settled here, many Jewish Christians believed that Gentile converts had to be circumcised like them and keep the Law of Moses, as well as believe in Jesus to be saved (cp Ac 15:1-2).