As far as I know, this isn't possible in the Vanilla version to the extent that you wish. If you could provide more information about what you want to be done that might help.
Using simple techniques without exploiting glitches that are very unreliable, it's not possible (As far as I know) to render anything on one client and not on another. I know particles have some rendering specifications but I very much doubt you want to make an entire gate out of particles. You can learn more about particles On the Minecraft Wiki. Sadly the way rendering works in Minecraft is that if it's in the game, everyone sees it.
Although there are ways to accomplish something like this.
Instancing is a game-based technique that places players in their own instance of a dungeon or room. Placing the open gate in a room separate from the closed gate and placing the players in the right location will achieve something similar to this. (I know this isn't exactly what instancing is, I don't know the proper terms for this. I play Minecraft, I don't make games). I know this might not be what you wanted but it is a solution.