The concept of quartal harmony can be applied in many ways on the piano. One application would be to combine quartal harmony with the study of modal scales. This is a good way to get aquanted with quartal harmony at a beginning level. Start by playing three pitch left handed chords on the piano that run through the Ionian scale. Voice the core scale tones in the bottom of the chord and stack two pitches (a fourth apart) above that. Keep all of your chord tones diatonic to the Ionian scale. Then try to apply this technique to the other modal scales.
Another exercise that can be useful in identifying quartal voicings is forming five part diatonic harmonies built down from the top pitch. With major seventh chords, a quartal voicing can be built down from every pitch of the major scale except the 4th (since it is an avoid tone). With minor and dominant seventh chords the options are more limited.
This Learning Music With Ray video discusses quartal chord voicings. In the video, I explain what quartal harmony is and how it can be applied to piano chord voicings. I provide visual examples of these voicings written on a musical staff. Finally, I demonstrate these applications of quartal voicings by playing them on the piano.