I have been studying John 15. Are the fruits we are to bear those in Galatians 5:22-23? And am I right to think that we should not ask for this fruit, because as believers we already have them?

Yes, you are correct that the fruit of John 15 are the fruit of the spirit of Galatians 5:22-23. But I do not think it would be correct to say that we already have this fruit, but rather we are to abide in Christ to be able to produce this fruit. We do not need to “ask for this fruit,” but we should be developing it as we grow spiritually.

In other words, when we believe, we have been given the Holy Spirit to indwell us. But now we must make a commitment to make Christ the Lord of our lives (Rom. 12:1-2), and then live a life in submission to the Spirit. When we do so, we will then begin producing the fruit of the spirit.

It does not come automatically with salvation. What comes automatically is the indwelling of the Holy Spirit. After that, we must live a life of both ongoing submission and study of the Word, as well as applying the Word, and, then, the fruit of the spirit will be produced in our lives.