This is me swimming.
Going a bit faster than my cruising speed. I'll do another one of that. Couple of weak points here when I try to go fast. Often when I 'slow down' or just really concentrate on perfect form, I'll just as fast.
The key to power is rotation. Use that rotation and your core strength to drive that leading arm down and forward into the water. Pull yourself over the point where your hand goes into the water. Build the power and speed of that arm until it is at pretty much full power at about 60% of the way through the pull. Drive the arm back and out at the same time giving a forceful kick with the same side foot/leg.
If you start that arm too fast when it first goes in, it will likely slip through the water, thus losing you a lot of thrust and power. You want to 'grab' as much of that water as you can. If your elbow is slightly higher than your hand going in, then you don't have to bend your wrist. Your hand should continue the curve of your arm. Feel the water on your palm. As the hand drives down and back at the same time.
If you bend your wrist or start pushing directly backwards too soon, just think of all that water you are not encompassing.
Questions?