One of the biggest contributors to shallowing the golf club in transition is to have depth. Depth is how far your hands move behind you in the backswing. If you look at the butt end of the club at address and the butt end of the club at the top of your swing, how much has that club moved behind you? The reason that’s so important is if you think about your club like a seesaw if my club is coming straight back down to the ball, that seesaw stands up or get steep but if my club back and my hands go towards the ball, the seesaw would drop down and shallow the club.
The best drill to help you create depth is to put a shaft over your shoulder. At address, put an alignment stick just outside your trail foot, about 6 to 12 inches off the target line. From there, go ahead and get that staff and put it right above your shoulder. You should be able to turn and make backswings without this shaft getting in the way of your lead arm. This will create proper depth, and proper depth leads to your better ability to shallow the golf club in transition.