I'm going to tell you how I developed my sharpness and hand speed.
If you're fairly experinced with how to throw a proper punch, start your form back at square one. Practice throwing with perfect form while keeping your body as loose as you possibly can. Do not try to force power into the punches at all, nor tighten up. Make sure your punch form is perfect in both delivery and timing of all the extra movements that make up a proper punch like the push from the back foot, the rotation of your hips, your front foot digging into the ground so you aren't carried by your own momentum until finally letting the compounded force travel out thru your shoulder. Make sure you have all the tiny motions in their correct sequence,, they should flow perfectly together once you get it down.
Now there's a key here that's hard to explain. You have to throw with a certain level of emptiness in your hands. Like you should be doing 0 pushing from your upper body, all the force should come from the rotation of your hips/torso. You should be initiating your punches from around your pelvis, maybe even your feet. Your arms and shoulders are just a vehicle for delivering the power from the lower body . When you do it right you should feel the force/weight transfer flowing through your arms. It'll feel like your limb is running or being carried by the movement. HOLD ON TO THAT FEELING, that is a measure of how potent your strike will be with any sort of MA move especially kicks.
Practice for a year or two throwing these kinds of punches and you'll wake up one day amazed at the difference. Also if you want to throw fastish combinations, intiate the beginning movements of the second attack as the first one is getting there. For example if you're throwing a fast 1-2, begin the cross with the pivot of your back foot just as the jab is getting there. shyt can look like god-mode hand speed some days lol