How can an element append into an empty array in java? [duplicate]

Your append(char[], char) method actually works. If you just run this example you will see there is no exception.

import java.util.*;
public class Test {
     public static void main(String[] args){
        char[] array = {};
        append(array, 'b');
     }
     
     
     static void append(char[] array, char x) {
       array = Arrays.copyOf(array, array.length + 1);
       array[array.length - 1] = x;
     }
}

So your error must be somewhere else. Most likely your append method should return the newly generated array:

import java.util.*;
public class Test {
     public static void main(String[] args){
        char[] array = {};
        array = append(array, 'b');
        array = append(array, 'c');
     }
     
     static char[] append(char[] array, char x) {
       array = Arrays.copyOf(array, array.length + 1);
       array[array.length - 1] = x;
       return array;
     }
}