Look up how to use a thumb ring or “dagger technique”. Hungarian, Mongols and pretty much all other fast shooting tribes used them.
Most horse bow archers hold their arrows in the hand they grip the bow with, completely cutting out the motions required to grab an arrow out of a quiver and nock it (Lajos Kassai does this)
You first want to develop the smoothest and most efficient shooting form you possibly can
This is how to do it
Look at your current form and find wasted motions (slowly positioning arrows under the knock point, slowly drawing the bow ect.) and find a way to make them more efficient without losing accuracy. Unnecessary motions= wasted time
Find a way to do two steps at once ( I swing draw and aim (split vision) in one motion, I also nock and arrow while positioning my body )
And finally (this will sound weird until I explain) learn how to shoot this form slow first and count off every step (1, 2, 3, 4 and release) you want to build up a consistent and SMOOTH form, and counting off helps your mind program your muscles. Speed comes with time and trying to learn smooth form with no wasted movements; while shooting fast will only result in lost arrows and missed targets.
I'm no master coach but that seems like the most common sense way do develop extremely fast shooting