Excellent advice from pax in post 2.
Part of learning to shoot faster is pushing yourself a little beyond your comfort level. Basically, as pax suggests, start by shooting at your comfortable pace, then pick up the pace a little. Your groups will open up some, but accept that. And don't go so fast that the groups are opening up too much. The finish by slowing up a bit to tighten your groups to where they were before. You'll be increasing your speed in manageable increments.
Do a lot of dry fire to build excellent trigger control. Excellent trigger control is critical. Conclude practice with a little slow fire to reinforce trigger control.
Also practice your presentation so that when you have brought your gun up the sights are aligned. At that point your using the sight picture to confirm sight alignment; you're not aiming. That's the "flash sight picture." Here's how Greg Morrison describes the flash sight picture (Morrison, Gregory, The Modern Technique of the Pistol
, Gunsite Press, 1991, pp 87 - 88, emphasis added):
...The flash sight-picture involves a glimpse of the sight-picture sufficient to confirm alignment....The target shooter’s gaze at the front sight has proven inappropriate for the bulk of pistolfighting. However, the practical shooter must start at this level and work up to the flash, which becomes reflexive as motor skills are refined. With practice, a consistent firing platform and firing stroke align the sights effortlessly. This index to the target eventually becomes an instantaneous confirmation of the sight-picture.
...Using the flash sight-picture programs the reflex of aligning the weapon’s sights with the target instantly....There is good reason for sights: one needs them to align the barrel with the target reliably....