I could never understand why there had to be a food shortage during Scar's reign as King, seems like a lot of bad things had to happen during Scar's reign as King, I also wished none of the bad things were happening during Scar's reign as King.
The problem was, Scar had plenty of ideas when it came to conquering a kingdom, but had no idea how to actually rule and manage things. Being king is a job, just like any other management position, and with it, comes responsibilities, responsibilities he wasn't willing to take on at all. One of those is feeding his subjects, and he had no interest in doing any of that beyond taking care of himself and his cronies, the hyenas.
From what I can tell, there was a drought going on, and the plant-eating herds of animals the lionesses usually hunted (and probably were forced to over-hunt, no thanks to Scar), had moved on to find grass to feed on, and they would have had to go beyond the borders of the Pridelands to find it.
But remember, this is all symbolic too. Remember how the Pridelands looked all dark, cloudy, and desolate when Scar ruled? That was meant to show that evil had come to the land, and because of his bad management, he had made the place barren. Similar situations like that have happened with bad rulers in real life, both past and present.
The horrible condition of the kingdom was meant to symbolize that scar was not qualified to be a ruler or King.
There was also a lot of mishaps:
Zazu was meant to be another set of eyes. He was a bird, who could fly! Therefore, he was a messager who warned everyone of danger.
But since Scar had him imprissoned behind bars (bones in this case), he couldn't do his job!
It's very likely that animals seen in "Circle of Life" we're scared of Scar! Remember Mufasa was generous in the sense of respecting all animals! Scar is a whole different person. Remember he tried to eat Zazu and the mouse in the beginning of the film and would've succeeded in Mufasa didn't arrive.
The decline of Pride Rock is tied to the age old myth of the King (the rightful one) is Tues to the land. When the King is in good health, his land is prosperous, when he is sickly or dies, so does his land until the next rightful king inherits the mantle. Watch Excalibur and see another example of this.
Even if the drought wasn't Scar's fault, you're forgetting one thing - he promised the hyenas they could hunt, kill, and eat as many animals as they want. Since the hyenas took over and over-hunted, the herds moved to find a safer home. That fact alone would leave the lions without food.