4 digits 7s display + 74HC595

Thank you, I was unable to follow your code, but wrote something that got it working, at least the first step.

const int digits = 4;

const int latchPin = 7;
const int clockPin = 6;
const int dataPin = 5;

const int digitOne = 8;
const int digitTwo = 9;
const int digitThree = 10;
const int digitFour = 11;

const byte digit[10] =
{
B10000001, //0 ----------
B11110011, //1 ----------
B01001001, //2 ----------
B01100001, //3 ----------
B00110011, //4 ----------
B00100101, //5 ----------
B00000101, //6 ----------
B11110001, //7 ----------
B00000001, //8 ----------
B00100001, //9 ----------
};

void setup() {

  pinMode(latchPin, OUTPUT);
  pinMode(clockPin, OUTPUT);
  pinMode(dataPin, OUTPUT);


  pinMode(digitOne, OUTPUT);  
  pinMode(digitTwo, OUTPUT);
  pinMode(digitThree, OUTPUT);
  pinMode(digitFour, OUTPUT);


  digitalWrite(digitOne, HIGH);
  digitalWrite(digitTwo, HIGH);
  digitalWrite(digitThree, HIGH);
  digitalWrite(digitFour, HIGH);  

}
  
void update_display() {
	for (int i = 0; i < 10; i++) 
	{

		digitalWrite(latchPin, LOW);
		shiftOut(dataPin, clockPin, MSBFIRST, digit[i]); 	
      	delay(200);
		digitalWrite(latchPin, HIGH);
	}
}

void loop () 
{
	update_display();
	delay(200);
}

Now I need to realize how to write over some specific digit and not the four at the same time