You need two things to accomplish what you want:
1) You need to be cooking a thicker cut of meat. The thinner sliced cuts of steak that I can usually afford makes it very hard to get a good crust on the outside while leaving the inside rare to medium rare. You need at least a good 3/4" or thicker cut of meat to even have a chance.
2) You need a very hot grill. Hotter than most gas grills can get. That means cooking over charcoal, with all of its associated hassles.
Remember that before you can brown and char the surface of the steak, you first have to boil off the water from the tissues. The hotter the grill, the faster the surface water will evaporate and allow the char you're looking for without letting the heat migrate to the inside of the steak too much.
If your grill isn't hot enough, then the heat has time to work its way to the inside of the steak before it can char the surface, giving you a more done center.
Some have tried using cast iron pans on their grill, and letting it get really hot. Cook the steak on the grill until you reach the internal doneness you desire, then move it to the hot skillet to provide the outside sear. I've not tried it but I have seen it recommended several times.
https://fieldcompany.com/blogs/journal/grilled-and-reverse-seared-cast-iron-skillet-steak
