Does the disciples' prayer still apply to Christians under grace?
Yes, the disciples' prayer still applies to Christians under grace, not as a mandatory formula but as a pattern. Although given under the Law to Jewish disciples, its format carries over because believers under grace still approach God's throne, giving Him His due and recognizing Him as their Almighty Heavenly Father.
Les explains that the prayer in Matthew 6 is commonly called the Lord's Prayer, but he prefers to call it the disciples' prayer because the Lord gave it as an example for the disciples to use, while the real Lord's Prayer is John 17. He notes it is a pattern, not a requirement to use exact words. At that time it was still under the Law, to the Jew under temple worship. Yet the format carries over into us under grace, because as we approach the throne room we still give God His due and recognize Him as the Almighty and our Heavenly Father. So we can certainly take note of it.
After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name.