We established that new heart is necessary for a Christian walk. That's the underlying assumption of the Epistles, we are new creations.
Now, as we read the New Testament with the assumption of new birth, we find a surprising feature: a new heart is necessary, but it's not sufficient. It's not just that God has given us new hearts and set us back to live better. No, God has placed us into an entirely new position: He's put us in a new place where the old rules just don't work.
When Moses brought the people to the Jordan river, he warned them that the rules for Canaan aren't the rules for Egypt (Deuteronomy 11:10–15). In Egypt they got crops by carrying water from the river out to the fields to water them. That won't work in Canaan, he warned. You can't force crops to grow in Canaan like you can in Egypt. In Canaan you depend on God for the crops: you rely on Him to bring the rains.
To use that language, we've come into a new land too: a land where human effort doesn't work. We've come to a place where we depend on God to send us the rains in season. So when we survey our lives and we don't see a lot of fruit there, we shouldn't decide we need better irrigation equipment. We need to heed Moses' warning: the rules are different here. What worked in Egypt won't work in Canaan.
Adam's creation is all about human effort: it's a lot like Moses described Egypt. If there's no water you just need to go out there and get some. The new creation's not like that. In fact, that sort of thing is counter-productive in the new creation.
So how do we get fruit in this new creation? The Lord Jesus said it very simply, "He that abides in me and I in him, *he* bears much fruit; for without me ye can do nothing" (John 15:4–5). In this new place where we've been brought, fruit is solely the result of abiding in Christ.
And so we're back to Philippians 3:9. What does it mean to be "in Christ?" It means to have nothing of our own to offer to God. It means we stand before God and say, "Christ is my righteousness". That's where fruit comes from in the new creation.