How should new covenant believers view and approach fasting?

There is definitely a place for fasting under the new covenant. The apostle Paul talked about fasting and described instances where he had fasted in Acts 14:23 and 27:21, and 2 Corinthians 11:27.

When fasting, the Lord Jesus Himself taught us that we are to keep it private between us and the Lord. He said, “When you fast, anoint your head and wash your face so that your fasting will not be noticed by men, but by your Father who is in secret” (Matt. 6:17–8).

So fasting under the new covenant is a time of private devotion that you have with the Lord. And like all other areas of your life, the Lord will lead and guide you whether to fast and when to fast.

I myself practice fasting. There are also times when I get so engrossed with studying and reading the Word of God in my own personal devotional time that I end up fasting unconsciously.

In the same way, if you are keen on fasting. I encourage you to let fasting be something you practice out of an intimate relationship with the Lord. It’s a beautiful thing to honor the Lord with your appetites.

Be wise though to not practice fasting legalistically or to judge and condemn others whom you may perceive to be less devoted to the Lord than you are. By all means, fast, but do it with grace, joy, revelation, and humility.