Sus chords
Sus chords became popular with jazz musicians in the 1960s. This was largely down to Herbie Hancocks use of them in the modal "Maiden Voyage" (1963), and McCoy Tyner's comping in songs such as "Naima" (1964).

A sus chord has a suspended fourth, and in most cases no third:

Difference in sound between fifth chords and sus chords

Although both fifth chords and sus chords don’t contain a 3rd, sus chords tend to have a more colourful, ambiguous sound because of the presence of the fourth tone. They often have extra tones added to them as well, e.g. a 9th. Whereas a fifth chord is usually played without any additional tones.

"Maiden Voyage" voicing
The modal song "Maiden Voyage" consists entirely of sus voicings. My interpretation of the opening chord of "Maiden Voyage" is show below: *

Sus chord sound
- The majority of Sus voicings don’t contain a 3rd. The 3rd note in a chord gives it either a major or minor quality. The lack of this note gives the chord an ambiguous and hollow sound. This is perfectly suited to most modal jazz songs, where an atmospheric "spacey" vibe is often desired.

- The lack of a 3rd means you have a lot of versatility in your choice of scale to use over this chord. It can be interpreted by the improviser as either minor or major. This is advantageous in a modal jazz song where you may want to use different modes to generate tension.  

- In traditional harmony, a suspended fourth usually resolves down to a major or minor third. However, in modal songs they often never resolve to a tonic style chord. This gives sus chords a searching or restless quality.

An easy way to think of the "Maiden Voyage" voicing on the piano is:

"Left Hand" - Root (D)
"Right Hand" - Triad whole-step below the root (C)

The triad in the right hand can be inverted for a "fuller" sound, as in the example above.

Parellelism
You can introduce parallelism, in a modal jazz song, by moving the same chords in the same direction. Parallelism can be diatonic or non-diatonic, depending on the level of tension you wish to introduce:

Diatonic
Play the C voicing starting on the 3rd, built up from perfect fourths, you learned in the "Fourth Chords" section. Take this chord “shape” and shift it about the piano keeping all the notes diatonic to the C Ionian mode. Don’t get too hung-up on keeping the exact intervals between each note in the chord, but focus more on keeping the overall shape of the chord as close to the original as possible. Notice how some voicings sound more dissonant than others due to the intervals between notes. This is a good technique to employ on a modal tune when the harmony is static and you need to introduce some tension to your comping to sustain interest.

Non-Diatonic
If you want to generate even more tension with you’re comping. Don’t replace any non-diatonic notes in a chord, built up from perfect fourths. For example, Play the C voicing starting on the root, built up from perfect fourths, you learned in the "Fourth Chords" section. Shift this chord “shape” around the piano. Notice how you slip in and out of different keys depending on the root note of the chord. This can sound really cool. Paradoxically, this non-diatonic tension can almost bring a sense a relief when dwelling on one chord for so long.  

* NOTE: This is the author's own work and represents their interpretation of the song. You may only use this information for private study, scholarship, or research.

3 note voicings
At this point you may think, using these voicings all my fingers are busy. How do I comp with fourth chords and solo at the same time? The answer is simple - just play a 3 note voicing in your left hand and solo in your right.

McCoy Tyner's signature lick
McCoy Tyner’s signature lick was to literally smash a root octave low down on the piano, and then play a 3-note left hand voicing while soloing in his right.

"So What" Chords
The Bill Evans piano voicing for “So What” is a fourth chord with a twist, i.e. it has a major third as it's top note. My interpretation is shown below: *

The trick here is to replace any perfect fourth, that falls "outside" the mode, with a tri-tone (b5). Or if it’s easier, think about this as a semitone up from a perfect fourth, or an augmented 4th. So Bb would now become B, etc. If you want stay diatonic to the mode, repeat this for every note that falls “outside” as you build up the chord: