Make sure your marksmanship fundamentals are strong, before trying to go fast. The only thing worse than fast misses are slow misses!
One good drill for fundamentals is the 5 and 1 drill. Do 5 dry fire shots, focusing on your fundamentals, then take 1 live fire shot doing the same. No time limit, and go for "perfect" shots. Repeat this cycle at least 5 times. It can get mentally fatiguing.
Once you get the accuracy you want, or better, start moving to a quicker pace. Challenge yourself to shoot as fast as you can, while still maintaining your desired accuracy.