Here is how to improve your draw time.
Try to listen and react to the start of the beep, most shot timers have a beep that lasts .30 seconds. If you are waiting for the beep to be over you are already loosing.
First work on reaction time only. Have your timer on your belt were your holster would be, at the beep move your hand to the timer and slap it as fast as you can.
Second, with your gun holstered, at the beep move your hand to the gun and establish a grip as fast as you can, do not draw, just get a grip. You should also be moving your support hand to a midpoint in front of your body.
Then start with a grip on your holstered gun, support hand at midpoint, and at the beep draw the gun and bring it to where your support hand will make contact and join the grip, do not come up to eye level or aim. As you can see we are breaking the process into sections.
Last, start with the gun at the point of your draw when your support hand joins the grip, and at the beep come up to eye level and get an appropriate sight picture and dry fire.
You can establish par times for each step, and work on small improvements on each one.