There are various exercises shown on how to maximize glute contraction by doing certain exercises. I am here to tell you that the single most important and pretty much the only effective exercise are deep squats. Yes, you have to go deep as low as you can. If your hips are too tight, foam roll them, warm up on the pre core and stretch out your hipnflexors and do this everyday for 15 minutes (warm up after foam rolling should be 5 min)
Make sure you are getting full rep ranges as you move through the range in motion. Do this for 3 sets of 20 reps at a moderately heavy weight.