The first quarter of the New World dealt with Haki, the second quarter of the new world dealth with Paramecia Awakenings, the third quarter dealt with Zoan Awakenings, so, next up is naturally Logia Awakenings.
My running theory is that Logia Awakenings are very powerful but very draining.
I'm pretty sure Kizaru's Awakening will be the ability to reflect, refract, and gather light to make it more powerful. It may also let him actually move at the speed of light, but for very brief periods.
I've said it before, I literally think Kizaru is going to grab the Laser Grid and use it as a weapon. Luffy might try the same thing, though. Yooooooo, light saber duel with Luffy and Kizaru? That would be hype.