Jarrett uses the sustain pedal fluidly to blend harmonies without letting them become muddy. Ensure you clear the pedal on major harmonic shifts, but allow the resonance to ring out during open intervals.
Without a specific PDF to reference, here is a general description of what one might find in an analysis of Keith Jarrett's "Shenandoah":
💡 : Compare the common Douglas Gould transcription with the official Scott Music version to see how different transcribers interpret his rubato timing.