When Paul describes his evangelistic strategy in 1 Corinthians 9, one of the things he is keen to point out is his flexibility with regard to the Jewish Law. He is content to keep it, if doing so will win a wider audience for the gospel; and he is content to ignore it, if that is the best way to get a hearing for the good news. However, he is very clear that he is essentially free from the Law of Moses - "To the Jews I became as a Jew, in order to win Jews. To those under the Law I became as one under the Law (though not being myself under the Law) that I might win those under the Law". I take it that the second sentence is just an amplification and explanation of the first - to win Jews, who are or at least regard themselves as being under the Law, Paul, who is not under that Law, acts as if he were under it.
This is remarkable enough in itself, given the faultless legal obedience of which the apostle feels able to speak elsewhere. It shows how completely Paul's outlook has changed with his conversion.
But to understand the direction in which it has changed, we need to read on. "To those outside the Law, I became as one outside the Law (not being outside the law of God but under the law of Christ)..." Paul has not become lawless in his conversion. Rather, he has moved from the domain of the Law of Moses into the domain of the Law of Christ. The latter is, of course, different in many ways - it is not codified but based on the gospel, it is not a burden but based on the completed work of Christ - but still, it absolutely claims Paul. In fact, his very chameleon like quality as an evangelist is an outworking of that Law of Christ - he must serve as Christ served, and he must take the gospel out to all because that is simply the logic of the good news.